Emeritus Professor Mark Gould
Emeritus Professor
School of Mathematics and Physics
Priestley Building (67), Room 660
Teaching and Learning
Professor Gould teaches 2nd and 4th year mathematics.
| Featured projects | Duration |
|---|---|
| Star quasi Hopf algebras | |
| Co-quasi Hopf algebras |
Book Chapters
Bracken, Anthony R., Gould, Mark D., Links, Jon R. and Zhang, Yao-Zhong (1999). Integrable models of correlated electrons. Statistical Physics on the Eve of the 21st Century. (pp. 303-315) edited by Murry Batchelor and Luc Wille. River Ridge, New Jersey United States: World Scientific Publishing. doi: 10.1142/3964
Bracken, Anthony J., Gould, Mark D., Zhang, Yao-Zhong and Delius, Gustav W. (1995). Infinite families of gauge-equivalent R-matrices and gradations of quantized affine algebras. Perspectives on Solvable Models. (pp. 231-243) Singapore, Singapore: World Scientific. doi: 10.1142/9789812831279_0015
Journal Articles
Gould, Mark D., Isaac, Phillip Simon and Werry, Jason (2022). Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras. Journal of Physics A: Mathematical and Theoretical, 55 (23) 235201, 235201. doi: 10.1088/1751-8121/ac6715
Gould, Mark and Pulemotov, Artem (2022). Homogeneous metrics with prescribed Ricci curvature on spaces with non-maximal isotropy. Communications in Analysis and Geometry, 30 (8), 1849-1893. doi: 10.4310/cag.2022.v30.n8.a8
Gould, Mark D. and Isaac, Phillip Simon (2019). Invariants and matrix elements of the quantum group Uq[gl(n, C)] revisited. Journal of Physics A: Mathematical and Theoretical, 52 (29) 295201, 295201. doi: 10.1088/1751-8121/ab2676
Feng, Jun, Zhang, Yao-Zhong, Gould, Mark D. and Fan, Heng (2018). Fine-grained uncertainty relations under relativistic motion. Europhysics Letters, 122 (6) 60001. doi: 10.1209/0295-5075/122/60001
Werry, Jason L., Isaac, Phillip S. and Gould, Mark D. (2017). Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond. Journal of Physics A: Mathematical and Theoretical, 50 (36) 365202, 365202. doi: 10.1088/1751-8121/aa8119
Werry, Jason L., Gould, Mark D. and Isaac, Phillip S. (2015). Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n). Journal of Mathematical Physics, 56 (12) 121703, 121703-1-121703-19. doi: 10.1063/1.4938076
Feng, Jun, Zhang, Yao-Zhong, Gould, Mark D. and Fan, Heng (2015). Uncertainty relation in Schwarzschild spacetime. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 743, 198-204. doi: 10.1016/j.physletb.2015.02.058
Gould, Mark D. and Isaac, Phillip S. (2015). Reduced matrix elements of the orthosymplectic Lie superalgebra. Journal of Physics A: Mathematical and Theoretical, 48 (2) 025201, 1-39. doi: 10.1088/1751-8113/48/2/025201
Feng, Jun, Zhang, Yao-Zhong, Gould, Mark D., Fan, Heng, Sun, Cheng-Yi and Yang, Wen-Li (2014). Probing Planckian physics in de Sitter space with quantum correlations. Annals of Physics, 351, 872-899. doi: 10.1016/j.aop.2014.10.014
Gould, Mark D., Isaac, Phillip S. and Werry, Jason L. (2014). Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n). Journal of Mathematical Physics, 55 (011703) 011703, 011703.1-011703.32. doi: 10.1063/1.4861706
Feng, Jun, Zhang, Yao-Zhong, Gould, Mark D. and Fan, Heng (2013). Entropic uncertainty relations under the relativistic motion. Physics Letters B, 726 (1-3), 527-532. doi: 10.1016/j.physletb.2013.08.069
Gould, Mark D., Isaac, Phillip S. and Werry, Jason L. (2013). Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n). Journal of Mathematical Physics, 54 (1) 013505, 013505. doi: 10.1063/1.4773573
Gould, Mark D., Taylor, Christopher, Wolff, Stephen K., Chandler, Graham S. and Jayatilaka, Dylan (2008). A definition for the covalent and ionic bond index in a molecule. Theoretical Chemistry Accounts, 119 (1-3), 275-290. doi: 10.1007/s00214-007-0282-x
Zhang, Shouchuan, Gould, Mark D. and Zhang, Yao-Zhong (2008). Local quasitriangular Hopf algebras. Symmetry, Integrability and Geometry: Methods and Applications, 4 042, 1-14. doi: 10.3842/SIGMA.2008.042
Dancer, K. A., Gould, M. D. and Links, J. (2007). Lax operator for the quantised orthosymplectic superalgebra Uq[osp(m\n)]. Algebras and Representation Theory, 10 (6), 593-617. doi: 10.1007/s10468-007-9049-2
Chen, Y. X., Gould, M. D. and Zhang, Y. Z. (2007). Finite matrix Model of Quantum Hall Fluids on S2. Bulletin of the Australian Mathematical Society, 76 (1), 111-132. doi: 10.1017/S0004972700039502
Dancer, K. A., Gould, M. D. and Links, J. (2006). Lax operator for the quantized orthosymplectic superalgebra Uq[osp(2|n)]. Journal of Statistical Mechanics: Theory and Experiment, 2006 (6) P06011, P06011-1-P06011-19. doi: 10.1088/1742-5468/2006/06/P06011
Burton, P. J. and Gould, M. D. (2006). Unitary R-matrices for topological quantum computing. Reports on Mathematical Physics, 57 (1), 89-96. doi: 10.1016/S0034-4877(06)80010-8
Mehta, M., Dancer, K. A., Gould, M. D. and Links, J. R. (2006). Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras. Journal of Physics A: Mathematical and General, 39 (1), L17-L26. doi: 10.1088/0305-4470/39/1/L03
Dancer, K. A., Gould, M. D. and Links, J. R. (2005). Eigenvalues of Casimir invariants for Uq[osp(m|n)]. Journal of Mathematical Physics, 46 (12) 123501, 123501-1-123501-20. doi: 10.1063/1.2137712
Zhang, Yao-Zhong and Gould, M. D. (2005). A unified and complete construction of all finite dimensional irreducible representations of gl(2|2). Journal of Mathematical Physics, 46 (1) 013505, 013505-1-013505-19. doi: 10.1063/1.1812829
Gould, MD and Lekatsas, T (2005). Some twisted results. Journal of Physics A-mathematical And General, 38 (47), 10123-10144. doi: 10.1088/0305-4470/38/47/006
Yang, W. L., Zhang, Y. Z. and Gould, M. D. (2004). Exact solution of the XXZ Gaudin model with generic open boundaries. Nuclear Physics B, 698 (3), 503-516. doi: 10.1016/j.nuclphysb.2004.07.029
Ding, Xiang-Mao, Gould, Mark D., Mewton, Courtney J. and Zhang, Yao-Zhong (2003). On osp(2|2) conformal field theories. Journal of Physics A-mathematical And General, 36 (11), 7649-7665. doi: 10.1088/0305-4470/36/27/316
Links, Jon, Zhou, Huan-Qiang, McKenzie, Ross H. and Gould, Mark D. (2003). Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins. Journal of Physics A: Mathematical and General, 36 (19), R63-R104. doi: 10.1088/0305-4470/36/19/201
Ding, X. M., Gould, M. D. and Zhang, Y. Z. (2003). gl(2 vertical bar 2) current superalgebra and non-unitary conformal field theory. Physics Letters A, 318 (4-5), 354-363. doi: 10.1016/j.physleta.2003.08.034
Ge, XY and Gould, MD (2003). Algebraic Bethe ansatz for integrable one-dimensional extended Hubbard models with open boundary conditions. Journal of Physics A-mathematical And General, 36 (7), 1801-1825. doi: 10.1088/0305-4470/36/7/302
Zhou, H. Q., Links, J., Gould, M. D. and McKenzie, R. H. (2003). Solvable models of Bose-Einstein condensates: A new algebraic Bethe ansatz scheme. Journal of Mathematical Physics, 44 (10), 4690-4701. doi: 10.1063/1.1605495
Gould, Mark D., Zhang, Yao-Zhong and Zhao, Shao-You (2002). Elliptic Gaudin models and elliptic KZ equations. Nuclear Physics B, 630 (3), 492-508. doi: 10.1016/S0550-3213(02)00136-0
Ding, Xiang-Mao, Gould, Mark D. and Zhang, Yao-Zhong (2002). Twisted parafermions. Physics Letters B, 530 (1-4), 197-201. doi: 10.1016/S0370-2693(02)01319-9
Zhou, Huan-Qiang, Links, Jon, McKenzie, Ross H. and Gould, Mark D. (2002). Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz. Physical Review B, 65 (6) 060502, 060502-1-060502-4. doi: 10.1103/PhysRevB.65.060502
Ding, XM, Gould, MD and Zhang, YZ (2002). A(2)((2)) parafermions: a new conformal field theory. Nuclear Physics B, 636 (3) 8334, 549-567. doi: 10.1016/S0550-3213(02)00335-8
Ge, X., Gould, M. D., Links, J. R. and Zhou, H. (2002). Reply to comment on `Integrable Kondo impurity in one-dimensional q-deformed t - J models. Journal of Physics A: Mathematical and General, 35 (29) 403, 6197-6201. doi: 10.1088/0305-4470/35/29/403
Links, J., Zhou, H. Q., McKenzie, R. H. and Gould, M. D. (2002). Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains. International Journal of Modern Physics B, 16 (23), 3429-3438. doi: 10.1142/S0217979202011949
Links, J. R., Zhou, H., Gould, M. D. and McKenzie, R. H. (2002). Integrability and exact spectrum of a pairing model for nucleons. Journal of Physics A: Mathematical and General, 35 (2) 317, 6459-6469. doi: 10.1088/0305-4470/35/30/317
Gould, M. D. and Zhang, Y. Z. (2002). R-matrices and the tensor product graph method. International Journal of Modern Physics B, 16 (14 & 15), 2145-2151. doi: 10.1142/S0217979202011901
Gould, M. D., Zhang, Y. Z. and Zhao, S. Y. (2002). Supersymmetric t-J Gaudin models and KZ equations. Journal of Physics A-mathematical And General, 35 (44), 9381-9393. doi: 10.1088/0305-4470/35/44/308
Ding, X. M., Gould, M. D. and Zhang, Y. Z. (2002). Free field and parafermionic realizations of twisted su(3)(k)((2)) current algebra. International Journal of Modern Physics B, 16 (14 & 15), 2153-2159. doi: 10.1142/S0217979202011913
Gould, Mark D., Zhang, Yao-Zhong and Isaac, Phillip S. (2001). On Quasi-Hopf Superalgebras. Communications in Mathematical Physics, 224 (2), 341-372. doi: 10.1007/s00220-001-0566-2
Bracken, Anthony J., Ge, Xiang-Yu, Gould, Mark D., Links, Jon and Zhou, Huan-Qiang (2001). Algebraic Bethe ansatz for integrable extended Hubbard models arising from supersymmetric group solutions. Journal of Physics A-mathematical And General, 34 (21), 4459-4474. doi: 10.1088/0305-4470/34/21/304
Links, Jon, Zhou, Huan-Qiang, McKenzie, Ross H. and Gould, Mark D. (2001). Ladder operator for the one-dimensional Hubbard model. Physical Review Letters, 86 (22), 5096-5099. doi: 10.1103/PhysRevLett.86.5096
Ge, X. Y., Gould, M. D., Links, J. and Zhou, H. Q. (2001). Integrable Kondo impurity in one-dimensional q-deformed t-J models. Journal of Physics A-mathematical And General, 34 (41), 8543-8561. doi: 10.1088/0305-4470/34/41/311
Ding, XM, Gould, MD and Zhang, YZ (2001). Twisted sl(3, C)(k)((2)) current algebra: free field representation and screening currents. Physics Letters B, 523 (3-4), 367-376. doi: 10.1016/S0370-2693(01)01361-2
Foerster, A, Gould, MD, Guan, XW, Roditi, I and Zhou, HQ (2001). Integrable open boundary conditions for the Bariev model of three coupled X Y spin chains. Nuclear Physics B, 612 (3), 461-478. doi: 10.1016/S0550-3213(01)00354-6
Bracken, A. J., Ge, X. Y., Gould, M. D. and Zhou, H. Q. (2001). Integrable extended hubbard models with boundary Kondo impurities. Bulletin of The Australian Mathematical Society, 64 (3), 445-467. doi: 10.1017/S0004972700019912
Zhou, H-Q, Ge, X. Y., Links, J. R. and Gould, M. D. (2000). Integrable Kondo impurities in one-dimensional extended Hubbard models. Physical Review B, 62 (8), 4906-4921. doi: 10.1103/PhysRevB.62.4906
Gould, M. D. and Zhang, Yao-Zhong (2000). Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices. Nuclear Physics B, 566 (3), 529-546. doi: 10.1016/S0550-3213(99)00516-7
Zhang, Yao-Zhong and Gould, M. D. (2000). Uq[sl(2|1)] vertex operators, screen currents and correlation functions at arbitrary level. Journal of Mathematical Physics, 41, 5277-5291.
Gould, Mark D., Zhang, Yao-Zhong and Isaac, Phillip S. (2000). Casimir invariants from quasi-Hopf (super)algebras. Journal of Mathematical Physics, 41 (1), 547-568. doi: 10.1063/1.533151
Links, JR, Gould, MD and Zhang, YZ (2000). Twisting invariance of link polynomials derived from ribbon quasi-Hopf algebras. Journal of Mathematical Physics, 41 (7), 5020-5032. doi: 10.1063/1.533390
Zhang, YZ and Gould, MD (2000). U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level. Journal of Mathematical Physics, 41 (8), 5277-5291. doi: 10.1063/1.533409
Zhang, YZ and Gould, MD (1999). Quasi-Hopf superalgebras and elliptic quantum supergroups. Journal of Mathematical Physics, 40 (10), 5264-5282. doi: 10.1063/1.533029
Zhou, H., Ge, X. and Gould, M. D. (1999). Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons. Journal of Physics A-mathematical And General, 32 (A), L137-L142. doi: 10.1088/0305-4470/32/12/002
Zhou, H., Ge, X. and Gould, M. D. (1999). Integrable Kondo impurities in the one-dimensional supersymmetric extended Hubbard model. Journal of Physics A: Mathematical and General, 32 (A), 5383-5388. doi: 10.1088/0305-4470/32/28/315
Gould, Mark D. and Zhang, Yao-Zhong (1999). Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules. Journal of Mathematical Physics, 40 (11), 5371-5386. doi: 10.1063/1.533075
Gould, MD and Stoilova, NI (1999). Eigenvalues of Casimir operators for gl(m/infinity). Journal of Physics A-mathematical And General, 32 (2), 391-399. doi: 10.1088/0305-4470/32/2/012
Zhou, H.Q., Ge, X.Y., Links, J and Gould, M.D. (1999). Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t-J model. Nuclear Physics B, 546 (3), 779-799. doi: 10.1016/S0550-3213(99)00085-1
Zhou, HQ and Gould, MD (1999). Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model. Physics Letters A, 251 (4), 279-285. doi: 10.1016/S0375-9601(98)00885-8
Burton, P. J. and Gould, M. D. (1998). Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis. International Journal of Quantum Chemistry, 66 (5), 323-343. doi: 10.1002/(SICI)1097-461X(1998)66:5
Ge, Xiang-Yu, Gould, Mark D., Zhang, Yao-Zhong and Zhou, Huan-Qiang (1998). Integrable eight-state supersymmetric U model with boundary terms and its Bethe ansatz solution. Physics Letters, Section A: General, Atomic and Solid State Physics, 238 (4-5), 309-314. doi: 10.1016/S0375-9601(97)00959-6
Burton, PJ and Gould, MD (1998). Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas. International Journal of Quantum Chemistry, 66 (5), 365-375. doi: 10.1002/(SICI)1097-461X(1998)66:5<365::AID-QUA3>3.0.CO;2-T
Delius, GW, Gardner, C and Gould, MD (1998). The structure of quantum Lie algebras for the classical series, B-l, C-l and D-l. Journal of Physics A-mathematical And General, 31 (8), 1995-2019. doi: 10.1088/0305-4470/31/8/012
Links, J, Hibberd, K, Gould, M and Foerster, A (1998). Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons. European Physical Journal B, 5 (3), 309-312. doi: 10.1007/s100510050447
Ge, XY, Gould, MD, Zhang, YZ and Zhou, HQ (1998). Integrable eight-state supersymmetric U model with boundary terms and its Bethe ansatz solution. Physics Letters A, 238 (4-5), 309-314. doi: 10.1016/S0375-9601(97)00959-6
Gould, MD and Zhang, YZ (1998). On super-RS algebra and Drinfeld realization of quantum affine superalgebras. Letters In Mathematical Physics, 44 (4), 291-308. doi: 10.1023/A:1007494602290
Ge, XY, Gould, MD, Zhang, YZ and Zhou, HQ (1998). A new two-parameter integrable model of strongly correlated fermions with quantum superalgebra symmetry. Journal of Physics A-mathematical And General, 31 (23), 5233-5239. doi: 10.1088/0305-4470/31/23/006
Gould, MD, Zhang, YZ and Zhou, HQ (1998). Eight-state supersymmetric U model of strongly correlated fermions. Physical Review B, 57 (16), 9498-9501. doi: 10.1103/PhysRevB.57.9498
Burton, PJ and Gould, MD (1998). Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs. International Journal of Quantum Chemistry, 66 (5), 345-363. doi: 10.1002/(SICI)1097-461X(1998)66:5<345::AID-QUA2>3.3.CO;2-I
Gould, MD, Links, JR, Zhang, YZ and Tsohantjis, I (1997). Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model. Journal of Physics A-mathematical And General, 30 (12), 4313-4325. doi: 10.1088/0305-4470/30/12/018
Gould, MD and Stoilova, NI (1997). Casimir invariants and characteristic identities for gl(infinity). Journal of Mathematical Physics, 38 (9), 4783-4793. doi: 10.1063/1.532123
Delius, GW and Gould, MD (1997). Quantum Lie algebras, their existence, uniqueness and q-antisymmetry. Communications In Mathematical Physics, 185 (3), 709-722. doi: 10.1007/s002200050107
Gould, MD and Links, JR (1997). Eigenvalues of Casimir invariants for unitary irreps of Uq(gl(m vertical bar n)). Journal of Physics A-mathematical And General, 30 (5), 1613-1627. doi: 10.1088/0305-4470/30/5/024
Links, JR and Gould, MD (1996). Integrable systems on open chains with quantum supersymmetry. International Journal of Modern Physics B, 10 (25), 3461-3480. doi: 10.1142/S0217979296001859
Delius, GW, Huffmann, A, Gould, MD and Zhang, YZ (1996). Quantum Lie algebras associated to U-q(gl(n)) and U-q(sl(n)). Journal of Physics A-Mathematical and General, 29 (17), 5611-5617. doi: 10.1088/0305-4470/29/17/031
Delius, GW, Gould, MD and Zhang, YZ (1996). Twisted quantum affine algebras and solutions to the Yang-Baxter equation. International Journal of Modern Physics a, 11 (19), 3415-3437. doi: 10.1142/S0217751X96001632
Gould, MD and Links, JR (1996). General eigenvalue formula for Casimir invariants of type I quantum superalgebras. Journal of Mathematical Physics, 37 (5), 2426-2456. doi: 10.1063/1.531519
Burton, PJ and Gould, MD (1996). Matrix elements of U(2n) generators in a multishell spin-orbit basis .1. General formalism. Journal of Chemical Physics, 104 (13), 5112-5133. doi: 10.1063/1.471139
Gould, MD, Links, JR and Zhang, YZ (1996). Eigenvalues of casimir invariants for type I quantum superalgebras. Letters in Mathematical Physics, 36 (4), 415-425. doi: 10.1007/BF00714406
Gould, Mark D., Hibberd, Katrina E., Links, Jon R. and Zhang, Yao-Zhong (1996). Integrable electron model with correlated hopping and quantum supersymmetry. Physics letters A, 212 (3), 156-160. doi: 10.1016/0375-9601(96)00042-4
Gould, MD, Links, JR and Zhang, YZ (1996). Type-I quantum superalgebras, q-supertrace, and two-variable link polynomials. Journal of Mathematical Physics, 37 (2), 987-1003. doi: 10.1063/1.531422
Hibberd, K. E., Gould, M. D. and Links, J. R. (1996). Algebraic Bethe ansatz for the supersymmetric U model. Physical Review B: Condensed Matter and Materials Physics, 54 (12), 8430-8437. doi: 10.1103/PhysRevB.54.8430
Links, JR and Gould, MD (1996). A q-superdimension formula for irreps of type I quantum superalgebras. Journal of Mathematical Physics, 37 (1), 484-492. doi: 10.1063/1.531403
Hibberd, KE, Gould, MD and Links, JR (1996). Algebraic Bethe ansatz for the anisotropic supersymmetric U model. Journal of Physics A-mathematical And General, 29 (24), 8053-8065. doi: 10.1088/0305-4470/29/24/028
Delius, GW, Gould, MD, Links, JR and Zhang, YZ (1995). Solutions of the Yang-Baxter Equation with Extra Nonadditive Parameters .2. U-Q(gl(m-Vertical-Bar-N)). Journal of Physics A-Mathematical and General, 28 (21), 6203-6210. doi: 10.1088/0305-4470/28/21/023
Lucht, MW and Gould, MD (1995). The Graphical Spin Algebra Method Applied to U(2N) Generators. Journal of Chemical Physics, 103 (13), 5590-5599. doi: 10.1063/1.470542
Delius, GW, Gould, MD, Links, JR and Zhang, YZ (1995). On Type-I Quantum Affine Superalgebras. International Journal of Modern Physics a, 10 (23), 3259-3281. doi: 10.1142/S0217751X95001571
Bracken, AJ, Gould, MD, Links, JR and Zhang, YZ (1995). New Supersymmetric and Exactly Solvable Model of Correlated Electrons. Physical Review Letters, 74 (14), 2768-2771. doi: 10.1103/PhysRevLett.74.2768
Bracken, AJ, Gould, MD and Zhang, YZ (1995). Quantized Affine Algebras and Parameter-Dependent R-Matrices. Bulletin of the Australian Mathematical Society, 51 (2), 177-194. doi: 10.1017/S0004972700014040
Gould, MD and Scheunert, M (1995). Classification of Finite-Dimensional Unitary Irreps for U-Q[Gl(M-Vertical-Bar-N)]. Journal of Mathematical Physics, 36 (1), 435-452. doi: 10.1063/1.531317
Links, JR and Gould, MD (1995). Classification of Unitary and Grade Star Irreps for U-Q(Osp(2-Vertical-Bar-2N)). Journal of Mathematical Physics, 36 (1), 531-545. doi: 10.1063/1.531321
Gould, MD (1994). Tensor Product Decompositions for Affine Kac-Moody Algebras. Reviews in Mathematical Physics, 6 (6), 1269-1299. doi: 10.1142/S0129055X94000456
Delius, GW, Gould, MD and Zhang, YZ (1994). On the Construction of Trigonometric Solutions of the Yang-Baxter Equation. Nuclear Physics B, 432 (1-2), 377-403. doi: 10.1016/0550-3213(94)90607-6
Gould, MD and Zhang, YZ (1994). Quantum Affine Lie-Algebras, Casimir Invariants, and Diagonalization of the Braid Generator. Journal of Mathematical Physics, 35 (12), 6757-6773. doi: 10.1063/1.530641
Links, JR, Scheunert, M and Gould, MD (1994). Diagonalization of the Braid Generator On Unitary Irreps of Quantum Supergroups. Letters in Mathematical Physics, 32 (3), 231-240. doi: 10.1007/BF00750665
Bracken, AJ, Gould, MD, Zhang, YZ and Delius, GW (1994). Infinite Families of Gauge-Equivalent R-Matrices and Gradations of Quantized Affine Algebras. International Journal of Modern Physics B, 8 (25-26), 3679-3691. doi: 10.1142/S0217979294001585
Bracken, AJ, Gould, MD, Zhang, YZ and Delius, GW (1994). Solutions of the Quantum Yang-Baxter Equation with Extra Nonadditive Parameters. Journal of Physics A-Mathematical and General, 27 (19) 025, 6551-6561. doi: 10.1088/0305-4470/27/19/025
Zhang, Y. Z. and Gould, M. D. (1994). On Universal R-Matrix for Quantized Nontwisted Rank-3 Affine Km Algebras (Vol 29, Pg 19, 1993). Letters in Mathematical Physics, 32 (1), 83-83.
Zhang, YZ and Gould, MD (1994). Quantum Affine Algebras and Universal R-Matrix with Spectral Parameter. Letters in Mathematical Physics, 31 (2), 101-110. doi: 10.1007/BF00750144
Gould, MD and Zhang, YZ (1994). Casimir Invariants for Quantized Affine Lie-Algebras. Letters in Mathematical Physics, 31 (1), 77-83. doi: 10.1007/BF00751173
Gould, MD, Paldus, J and Cizek, J (1994). Quasi-Spin and the Pseudo-Orthogonal Group in the Hubbard-Model. International Journal of Quantum Chemistry, 50 (3), 207-231. doi: 10.1002/qua.560500306
Tsohantjis, I and Gould, MD (1994). Quantum Double Finite-Group Algebras and Link Polynomials. Bulletin of the Australian Mathematical Society, 49 (2), 177-204. doi: 10.1017/S0004972700016270
Gould, MD and Zhang, YZ (1994). Quantized Affine Lie-Algebras and Diagonalization of Braid Generators. Letters in Mathematical Physics, 30 (4), 267-277. doi: 10.1007/BF00751063
Zhang, YZ and Gould, MD (1993). Unitarity and Complete Reducibility of Certain Modules Over Quantized Affine Lie-Algebras. Journal of Mathematical Physics, 34 (12), 6045-6059. doi: 10.1063/1.530249
Gould, MD and Battle, JS (1993). Spin-Dependent Unitary-Group Approach .2. Derivation of Matrix-Elements for Spin-Dependent Operators. Journal of Chemical Physics, 99 (8), 5961-5975. doi: 10.1063/1.465895
Gould, MD and Battle, JS (1993). Spin-Dependent Unitary-Group Approach to the Pauli-Breit Hamiltonian .2. 1St-Order Energy-Level Shifts Due to Spin-Spin Interaction. Journal of Chemical Physics, 99 (8), 5983-5994. doi: 10.1063/1.465897
Gould, MD (1993). Quantum Double Finite-Group Algebras and Their Representations. Bulletin of the Australian Mathematical Society, 48 (2), 275-301. doi: 10.1017/S0004972700015707
Gould, MD, Tsohantjis, I and Bracken, AJ (1993). Quantum Supergroups and Link Polynomials. Reviews in Mathematical Physics, 5 (3), 533-549. doi: 10.1142/S0129055X93000152
Zhang, YZ and Gould, MD (1993). On Universal R-Matrix for Quantized Nontwisted Rank 3 Affine Km Algebras. Letters in Mathematical Physics, 29 (1), 19-32. doi: 10.1007/BF00760855
Paldus, J and Gould, MD (1993). Unitary-Group Approach to Reduced Density-Matrices .2. One-Electron Charge and Spin-Density Algebra. Theoretica Chimica Acta, 86 (1-2), 83-96. doi: 10.1007/BF01113516
Gould, MD and Battle, JS (1993). Spin-Dependent Unitary-Group Approach to the Pauli-Breit Hamiltonian .1. 1St-Order Energy-Level Shifts Due to Spin-Orbit Interactions. Journal of Chemical Physics, 98 (11), 8843-8851. doi: 10.1063/1.464494
Links, JR, Gould, MD and Zhang, RB (1993). Quantum Supergroups, Link Polynomials and Representation of the Braid Generator. Reviews in Mathematical Physics, 5 (2), 345-361. doi: 10.1142/S0129055X93000097
Gould, MD, Zhang, RB and Bracken, AJ (1993). Quantum Double Construction for Graded Hopf-Algebras. Bulletin of the Australian Mathematical Society, 47 (3), 353-375. doi: 10.1017/S0004972700015197
Bracken, AJ, Gould, MD and Tsohantjis, I (1993). Boson-Fermion Models for Osp(1,2) and Uq[Osp(1,2)]. Journal of Mathematical Physics, 34 (5), 1654-1664. doi: 10.1063/1.530182
Links, J. and Gould, M. D. (1993). Raising and lowering operators for Uq(gl(n)). Journal of Mathematical Physics, 34 (4), 1577-1586. doi: 10.1063/1.530175
Battle, JS and Gould, MD (1993). Formulas for the Spin-Dependent Unitary-Group Approach. Chemical Physics Letters, 201 (1-4), 284-293. doi: 10.1016/0009-2614(93)85072-V
Links, JR, Gould, MD and Tsohantjis, I (1993). Baxterization of the R-Matrix for the Adjoint Representation of Uq[D(2, 1-Alpha)]. Letters in Mathematical Physics, 27 (1), 51-58. doi: 10.1007/BF00739589
Gould, Mark and Biedenharn, L. C. (1992). The pattern calculus for tensor operators in quantum groups. Journal of Mathematical Physics, 33 (11), 3613-3635. doi: 10.1063/1.529909
Links, JR and Gould, MD (1992). 2 Variable Link Polynomials From Quantum Supergroups. Letters in Mathematical Physics, 26 (3), 187-198. doi: 10.1007/BF00420752
Burton, PJ and Gould, MD (1992). A Unitary-Group Formulation of the Complete Active Space Configuration-Interaction Method .2. An Approach Based On the Subgroup Chain U(N=N0+N1+N2)Superset-of-or-Equal-to-U(N0)Xu(N1+N2)Superset-of-or-Equal-to-U(N0)Xu(N1)Xu(N2). Journal of Chemical Physics, 96 (7), 5261-5271. doi: 10.1063/1.462711
Gould, M. D., Links, J. and Bracken, A. J. (1992). Matrix elements and Wigner coefficients for Uq[gl(n)]. Journal of Mathematical Physics, 33 (3), 1008-1022. doi: 10.1063/1.529986
Gould, MD (1992). Reduced Wigner Coefficients for Uq(Gl(N)). Journal of Mathematical Physics, 33 (3), 1023-1031. doi: 10.1063/1.529764
Gould, MD (1992). Quantum Groups and Diagonalization of the Braid Generator. Letters in Mathematical Physics, 24 (3), 183-196. doi: 10.1007/BF00402893
Links, J. R. and Gould, M. D. (1992). Casimir invariants for Hopf algebras. Reports on Mathematical Physics, 31 (1), 91-111. doi: 10.1016/0034-4877(92)90007-N
Zhang, RB and Gould, MD (1991). Universal-R Matrices and Invariants of Quantum Supergroups. Journal of Mathematical Physics, 32 (12), 3261-3267. doi: 10.1063/1.529487
Gould, MD, Zhang, RB and Bracken, AJ (1991). Generalized Gelfand Invariants and Characteristic Identities for Quantum Groups. Journal of Mathematical Physics, 32 (9), 2298-2303. doi: 10.1063/1.529152
Gould, MD and Jarvis, PD (1991). Characteristic Identities for Kac-Moody Algebras. Letters in Mathematical Physics, 22 (2), 91-100. doi: 10.1007/BF00405172
Zhang, RB, Gould, MD and Bracken, AJ (1991). From Representations of the Braid Group to Solutions of the Yang-Baxter Equation. Nuclear Physics B, 354 (2-3), 625-652. doi: 10.1016/0550-3213(91)90369-9
Bracken, AJ, McAnally, DS, Zhang, RB and Gould, MD (1991). A Q-Analog of Bargmann Space and its Scalar Product. Journal of Physics A-Mathematical and General, 24 (7) 015, 1379-1391. doi: 10.1088/0305-4470/24/7/015
Zhang, RB, Gould, MD and Bracken, AJ (1991). Generalized Gelfand Invariants of Quantum Groups. Journal of Physics A-Mathematical and General, 24 (5) 009, 937-943. doi: 10.1088/0305-4470/24/5/009
Zhang, RB, Bracken, AJ and Gould, MD (1991). Solution of the Graded Yang-Baxter Equation Associated with the Vector Representation of Uq(Osp(M/2N)). Physics Letters B, 257 (1-2), 133-139. doi: 10.1016/0370-2693(91)90870-V
Zhang, RB, Gould, MD and Bracken, AJ (1991). Solutions of the Graded Classical Yang-Baxter Equation and Integrable Models. Journal of Physics A-Mathematical and General, 24 (6), 1185-1197. doi: 10.1088/0305-4470/24/6/012
Gould, M. D. (1991). Classification of infinite dimensional irreducible modules for type I Lie superalgebras. Reports on Mathematical Physics, 30 (3), 363-380. doi: 10.1016/0034-4877(91)90065-U
Zhang, RB, Gould, MD and Bracken, AJ (1991). Quantum Group Invariants and Link Polynomials. Communications in Mathematical Physics, 137 (1), 13-27. doi: 10.1007/BF02099115
Gould, MD, Jarvis, PD and Bracken, AJ (1990). Branching-Rules for a Class of Typical and Atypical Representations of Gl(M/n). Journal of Mathematical Physics, 31 (12), 2803-2810. doi: 10.1063/1.528983
Gould, MD and Zhang, RB (1990). Classification of All Star Irreps of Gl(M-N). Journal of Mathematical Physics, 31 (11), 2552-2559. doi: 10.1063/1.529001
Gould, MD and Zhang, RB (1990). Unitary Representations of Basic Classical Lie-Superalgebras. Letters in Mathematical Physics, 20 (3), 221-229. doi: 10.1007/BF00398365
Gould, MD, Paldus, J and Chandler, GS (1990). Unitary-Group Approach to Reduced Density-Matrices. Journal of Chemical Physics, 93 (6), 4142-4153. doi: 10.1063/1.458747
Zhang, RB and Gould, MD (1990). Classification of Star and Grade-Star Representations of C(N+1). Journal of Mathematical Physics, 31 (8), 1889-1894. doi: 10.1063/1.528687
Gould, M. D. and Zhang, R. B. (1990). Classification of all star and grade irreps of gl(n/1). Journal of Mathematical Physics, 31 (6), 1524-1534. doi: 10.1063/1.528695
Gould, MD and Paldus, J (1990). Spin-Dependent Unitary-Group Approach .1. General Formalism. Journal of Chemical Physics, 92 (12), 7394-7401. doi: 10.1063/1.458225
Bracken, AJ, Gould, MD and Zhang, RB (1990). Quantum Supergroups and Solutions of the Yang-Baxter Equation. Modern Physics Letters a, 5 (11), 831-840. doi: 10.1142/S0217732390000925
Gould, MD, Bracken, AJ and Hughes, Jwb (1989). Branching-Rules for Typical and Atypical Representations of Gl(N/1). Journal of Physics A-Mathematical and General, 22 (15), 2879-2896. doi: 10.1088/0305-4470/22/15/008
Gould, MD (1989). Representation-Theory of the Symplectic Groups .1.. Journal of Mathematical Physics, 30 (6), 1205-1218. doi: 10.1063/1.528346
Gould, MD (1989). Atypical Representations for Type-I Lie-Superalgebras. Journal of Physics A-Mathematical and General, 22 (9) 012, 1209-1221. doi: 10.1088/0305-4470/22/9/012
Gould, MD and Chandler, GS (1989). A Unitary-Group Formulation of the Complete Active Space Configuration-Interaction Method .1. General Formalism. Journal of Chemical Physics, 90 (7), 3680-3685. doi: 10.1063/1.455825
Gould, M. D. (1989). Casimir invariants and infinitesimal characters for semi-simple Lie algebras. Reports on Mathematical Physics, 27 (1), 73-111. doi: 10.1016/0034-4877(89)90037-2
Gould, MD and Paldus, J (1987). Parastatistics and the Clifford-Algebra Unitary-Group Approach to the Many-Electron Correlation-Problem. Journal of Mathematical Physics, 28 (10), 2304-2309. doi: 10.1063/1.527762
Gould, MD (1987). Identities and Characters for Finite-Groups. Journal of Physics A-Mathematical and General, 20 (10), 2657-2665. doi: 10.1088/0305-4470/20/10/009
Gould, MD (1987). Reduced Characters for Finite-Groups. Molecular Physics, 60 (5), 991-1014. doi: 10.1080/00268978700100661
Gould, MD and Chandler, GS (1987). Bases for the Irreducible Representations of O(3) Symmetry Adapted to a Crystallographic Point Group. International Journal of Quantum Chemistry, 31 (3), 535-563. doi: 10.1002/qua.560310323
Gould, MD (1987). Polynomial-Identities for Simple Lie-Superalgebras. Journal of the Australian Mathematical Society Series B-Applied Mathematics, 28 (3), 310-327. doi: 10.1017/S0334270000005427
Gould, MD and Paldus, J (1986). Unitary-Group Approach to General System Partitioning .1. Calculation of U(N = N1 + N2) - U(N1) X U(N2) Reduced Matrix-Elements and Reduced Wigner Coefficients. International Journal of Quantum Chemistry, 30 (3), 327-363. doi: 10.1002/qua.560300304
Gould, MD (1986). Unitary-Group Approach to General System Partitioning .2. U(N) Matrix Element Evaluation in a Composite Basis. International Journal of Quantum Chemistry, 30 (3), 365-389. doi: 10.1002/qua.560300305
Gould, M. D. (1986). Multiplicity-free Wigner coefficients for semisimple Lie-groups. II. A pattern calculus for O(n). Journal of Mathematical Physics, 27 (8), 1964-1979. doi: 10.1063/1.527014
Gould, MD and Paldus, J (1986). Para-Fermi Algebras and the Many-Electron Correlation-Problem. Physical Review a, 34 (2), 804-814. doi: 10.1103/PhysRevA.34.804
Gould, MD (1986). Multiplicity-Free Wigner Coefficients for Semisimple Lie-Groups .1. the U(N) Pattern Calculus. Journal of Mathematical Physics, 27 (8), 1944-1963. doi: 10.1063/1.527013
Gould, MD and Edwards, SA (1986). A Projection Based Approach to the Clebsch-Gordan Multiplicity Problem for Compact Semisimple Lie-Groups .3. the Classical Limit. Journal of Physics A-Mathematical and General, 19 (9), 1537-1544. doi: 10.1088/0305-4470/19/9/024
Edwards, SA and Gould, MD (1986). A Projection Based Approach to the Clebsch-Gordan Multiplicity Problem for Compact Semisimple Lie-Groups .2. Application to U(N). Journal of Physics A-Mathematical and General, 19 (9), 1531-1536. doi: 10.1088/0305-4470/19/9/023
Edwards, SA and Gould, MD (1986). A Projection Based Approach to the Clebsch-Gordan Multiplicity Problem for Compact Semisimple Lie-Groups .1. General Formalism. Journal of Physics A-Mathematical and General, 19 (9), 1523-1529. doi: 10.1088/0305-4470/19/9/022
GOULD, MD (1985). CORRECTION. International Journal of Quantum Chemistry, 27 (6), 787-801. doi: 10.1002/qua.560270613
Gould, MD (1985). Characteristic Identities for Semi-Simple Lie-Algebras. Journal of the Australian Mathematical Society Series B-Applied Mathematics, 26 (JAN), 257-283. doi: 10.1017/S0334270000004501
Gould, MD and Kalnins, EG (1985). A Projection-Based Solution to the Sp(2N) State Labeling Problem. Journal of Mathematical Physics, 26 (7), 1446-1457. doi: 10.1063/1.526908
Gould, MD (1985). Correction. International Journal of Quantum Chemistry, 27 (6), 787-801. doi: 10.1002/qua.560270613
Gould, MD and Chandler, GS (1984). A Spin-Dependent Unitary-Group Approach to Many-Electron Systems. International Journal of Quantum Chemistry, 26 (4), 441-455. doi: 10.1002/qua.560260403
Gould, MD and Chandler, GS (1984). Unitary-Group Approach to the Many-Electron Problem .2. Adjoint Tensor-Operators for U(N). International Journal of Quantum Chemistry, 25 (3), 603-633. doi: 10.1002/qua.560250312
Gould, MD and Chandler, GS (1984). Unitary-Group Approach to the Many-Electron Problem .1. Matrix Element Evaluation and Shift-Operators. International Journal of Quantum Chemistry, 25 (3), 553-601. doi: 10.1002/qua.560250311
Gould, MD and Edwards, SA (1984). Enveloping Algebra Annihilators and Projection Techniques for Finite-Dimensional Cyclic Modules of a Semisimple Lie-Algebra. Journal of Mathematical Physics, 25 (10), 2848-2855. doi: 10.1063/1.526033
Gould, MD (1984). Tensor-Operators and Projection Techniques in Infinite Dimensional Representations of Semi-Simple Lie-Algebras. Journal of Physics A-Mathematical and General, 17 (1), 1-17. doi: 10.1088/0305-4470/17/1/006
Gould, MD and Chandler, GS (1984). Unitary-Group Approach to the Many-Electron Problem .3. Matrix-Elements of Spin-Dependent Hamiltonians. International Journal of Quantum Chemistry, 25 (6), 1089-1109. doi: 10.1002/qua.560250613
Gould, MD (1981). Wigner Coefficients for a Semisimple Lie Group and the Matrix-Elements of the O(N) Generators. Journal of Mathematical Physics, 22 (11), 2376-2388. doi: 10.1063/1.524820
Gould, MD (1981). On the Matrix-Elements of the U(N) Generators. Journal of Mathematical Physics, 22 (1), 15-22. doi: 10.1063/1.524749
Gould, MD (1981). General U(N) Raising and Lowering Operators. Journal of Mathematical Physics, 22 (2), 267-270. doi: 10.1063/1.524898
Gould, MD (1980). Infinitesimal Approach to Semisimple Lie-Groups and Raising and Lowering Operators of O(N) and U(N). Journal of Mathematical Physics, 21 (3), 444-453. doi: 10.1063/1.524441
Gould, MD (1978). Applications of Characteristic Identity for Gl(N). Annales De L Institut Henri Poincare Section a Physique Theorique, 29 (1), 51-83.
Conference Papers
Isaac, Phillip S., Werry, Jason L. and Gould, Mark D. (2015). Characteristic identities for Lie (super)algebras. 30th International Colloquium on Group Theoretical Methods in Physics (Group30), Ghent Belgium, 14-18 July, 2014. Bristol, United Kingdom: Institute of Physics Publishing. doi: 10.1088/1742-6596/597/1/012045
Hibberd, KE, Gould, MD and Links, JR (1998). U-q[gl(2 vertical bar 1)] and the anisotropic supersymmetric U model. 12th International Colloquium on Group Theoretical Methods in Physics (Group 22), Hobart Australia, Jul 13-17, 1998. CAMBRIDGE: INTERNATIONAL PRESS INC BOSTON.
Gould, MD and Isaac, PS (1998). Quasi-Lie algebras and a method for determining non-degeneracy of the quasi-Lie product. 12th International Colloquium on Group Theoretical Methods in Physics (Group 22), Hobart Australia, Jul 13-17, 1998. CAMBRIDGE: INTERNATIONAL PRESS INC BOSTON.
Hibberd, KE, Links, JR and Gould, MD (1997). The supersymmetric U model and Bethe ansatz equations. XXI International Colloquium on Group Theoretical Methods in Physics - Group 21, Goslar Germany, Jul 15-20, 1996. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD.
Gould, M. D. (1995). Quantum groups and link polynomials. Confronting the Infinite, Adelaide, SA, Australia, 14-17 February, 1994. River Edge, NJ, USA: World Scientific Publishing.
Gould, M. D. (1995). Quantum groups for physicists. Statistical Mechanics and Field Theory: The 7th Physics Summer School, Canberra, ACT, Australia, 10-28 January, 1994. River Edge, NJ, USA: World Scientific Publications.