Dr Phillip Isaac
Senior Lecturer
School of Mathematics and Physics
+61 7 336 53267
Priestley Building (67), Room 743
Personal page
Dr Phillip Isaac's personal page
Teaching and learning
Dr Isaac teaches into 2nd and 3rd year mathematics including mathematical analyis, calculus and linear algebra, and partial differential equations.
Researcher biography
Dr Phillip Isaac is a mathematician interested in algebraic structures, particularly those related to quantum integrable systems.
Phillip received his PhD in mathematics in May 2001 from UQ. The title of his thesis was "Quasi Hopf superalgebras and their dual structures".
He worked as a JAVA programmer/cryptographer for about 9 months before undertaking a postdoctoral research fellowship at the Graduate School of Mathematical Sciences, University of Tokyo, Japan. His project was entitled "Symmetries in quantum spin chains".
After his return to Australia in September 2003, he began casual employment at UQ, working as a first year tutor and developing course materials.
His current research activities involve developing the constructive representation theory of Lie (super)algebras, quantum groups and related structures, and its utility in application, particularly to quantum integrable systems.
Journal Articles
Jones, Mitchell, Isaac, Phillip S. and Links, Jon (2024). An integrability illusion: vanishing transfer matrices associated with generalised Gaudin superalgebras. Nuclear Physics B, 1008 116706, 116706. doi: 10.1016/j.nuclphysb.2024.116706
Bennett, Lachlan, Foerster, Angela, Isaac, Phillip S. and Links, Jon (2024). Occupancy probabilities in superintegrable bosonic networks. Nuclear Physics B, 998 116406, 116406. doi: 10.1016/j.nuclphysb.2023.116406
Almutairi, Alhanouf M. and Isaac, Phillip S. (2024). A connection between Uq(sl(3)) and Z2×Z2-graded special linear Lie colour algebras via Klein operators. Journal of Mathematical Physics, 65 (1) ARTN 013503. doi: 10.1063/5.0163904
Bennett, Lachlan, Isaac, Phillip Simon and Links, Jon (2023). NOON state measurement probabilities and outcome fidelities: a Bethe Ansatz approach. Journal of Physics A: Mathematical and Theoretical, 56 (50) 505202, 1-27. doi: 10.1088/1751-8121/ad0a71
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
Aizawa, N., Isaac, P. S. and Segar, J. (2020). ℤ2 × ℤ2-Generalizations of Infinite-Dimensional Lie Superalgebra of Conformal Type with Complete Classification of Central Extensions. Reports on Mathematical Physics, 85 (3), 351-373. doi: 10.1016/S0034-4877(20)30041-0
Shen, Yibing, Isaac, Phillip and Links, Jon (2020). Ground-state energy of a Richardson-Gaudin integrable BCS model. SciPost Physics Core, 2 (1) 001. doi: 10.21468/scipostphyscore.2.1.001
Isaac, Phillip S., Stoilova, N. I. and Van der Jeugt, Joris (2020). The Z2×Z2-graded general linear Lie superalgebra. Journal of Mathematical Physics, 61 (1) 011702, 011702. doi: 10.1063/1.5138597
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
Aizawa, N., Isaac, P. S. and Segar, J. (2019). Z2×Z2 generalizations of N=1 superconformal Galilei algebras and their representations. Journal of Mathematical Physics, 60 (2) 023507, 023507. doi: 10.1063/1.5054699
Alshammari, Fahad, Isaac, Phillip S. and Marquette, Ian (2019). On Casimir operators of conformal Galilei algebras. Journal of Mathematical Physics, 60 (1) 013509, 013509. doi: 10.1063/1.5064840
Shen, Yibing, Isaac, Phillip S. and Links, Jon (2018). Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz. Nuclear Physics B, 937, 28-55. doi: 10.1016/j.nuclphysb.2018.08.015
Agboola, Davids, Isaac, Phillip Simon and Links, Jon (2018). Energy-level crossings and number-parity effects in a bosonic tunneling model. Journal of Physics B: Atomic, Molecular and Optical Physics, 51 (14) 145301, 145301. doi: 10.1088/1361-6455/aac6f2
Alshammari, Fahad, Isaac, Phillip S. and Marquette, Ian (2018). A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras. Journal of Physics A: Mathematical and Theoretical, 51 (6) 065206, 065206. doi: 10.1088/1751-8121/aaa468
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
Rubeni, D., Links, J., Isaac, P. S. and Foerster, A. (2017). Two-site Bose-Hubbard model with nonlinear tunneling: classical and quantum analysis. Physical Review A, 95 (4) 043607. doi: 10.1103/PhysRevA.95.043607
Lukyanenko, Inna, Isaac, Phillip S. and Links, Jon (2016). An integrable case of the p + ip pairing Hamiltonian interacting with its environment. Journal of Physics A-Mathematical and Theoretical, 49 (8) 084001. doi: 10.1088/1751-8113/49/8/084001
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
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
Lukyanenko, Inna, Isaac, Phillip S. and Links, Jon (2014). On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system. Nuclear Physics B, 886, 364-398. doi: 10.1016/j.nuclphysb.2014.06.018
Isaac, Phillip S. and Marquette, Ian (2014). On realizations of polynomial algebras with three generators via deformed oscillator algebras. Journal of Physics A: Mathematical and Theoretical, 47 (20) 205203, 1-26. doi: 10.1088/1751-8113/47/20/205203
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
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
Aizawa, Naruhiko, Isaac, Phillip S. and Kimura, Yuta (2012). Highest weight representations and Kac determinants for a class of conformal galilei algebras with central extension. International Journal of Mathematics, 23 (11) 1250118, 1250118.1-1250118.25. doi: 10.1142/S0129167X12501182
Andrew Birrell, Isaac, Phillip and Links, Jon R. (2012). A variational approach for the quantum inverse scattering method. Inverse Problems, 28 (3) 035008, 035008.1-035008.15. doi: 10.1088/0266-5611/28/3/035008
Dunning, Clare, Isaac, Phillip S., Links, Jon and Zhao, Shao-You (2011). BEC-BCS crossover in a (p + ip)-wave pairing Hamiltonian coupled to bosonic molecular pairs. Nuclear Physics B, 848 (2), 372-397. doi: 10.1016/j.nuclphysb.2011.03.001
Finch, P. E., Dancer, K. A., Isaac, P. S. and Links, J. (2011). Solutions of the Yang-Baxter equation: Descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras. Nuclear Physics Section B, 847 (2), 387-412. doi: 10.1016/j.nuclphysb.2011.01.034
Aizawa, N and Isaac, PS (2011). On irreducible representations of the exotic conformal Galilei algebra. Journal of Physics A-Mathematical and Theoretical, 44 (3) 035401, 1-8. doi: 10.1088/1751-8113/44/3/035401
Campbell, C. W., Dancer, K. A., Isaac, P. S. and Links, J. (2010). Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D-3) symmetry. Nuclear Physics, Section B, 836 (3), 171-185. doi: 10.1016/j.nuclphysb.2010.04.014
Dancer, K. A., Finch, P. E., Isaac, P. S. and Links, J. (2009). Integrable boundary conditions for a non-Abelian anyon chain with D(D3) symmetry. Nuclear Physics B, 812 (3), 456-469. doi: 10.1016/j.nuclphysb.2008.12.002
Tonkes, E. J., Isaac, P. S. and Scharaschkin, V. (2009). Assessment of an innovative system of lecture notes in first-year mathematics. International Journal of Mathematical Education in Science and Technology, 40 (4), 495-504. doi: 10.1080/00207390902759592
Dancer, K. A., Finch, P. E. and Isaac, P. S. (2007). Universal Baxterization for Z-graded Hopf algebras. Journal of Physics A: Mathematical and Theoretical, 40 (50), F1069-F1075. doi: 10.1088/1751-8113/40/50/F01
Isaac, P. S., Joyce, W. P. and Links, J. (2007). An algebraic approach to symmetric pre-monoidal statistics. Journal of Algebra and Its Applications, 6 (1), 49-69. doi: 10.1142/S0219498807002065
Dancer, K. A., Isaac, P. S. and Links, J. (2006). Representations of the quantum doubles of finite group algebras and spectral parameter dependent solutions of the Yang–Baxter equation. Journal of Mathematical Physics, 47 (10) 103511, 103511-1-103511-18. doi: 10.1063/1.2359575
Aizawa, N and Isaac, PS (2003). Weak Hopf algebras corresponding to U-q[sl(n)]. Journal of Mathematical Physics, 44 (11), 5250-5267. doi: 10.1063/1.1616999
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
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
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
Birrell, A., Isaac, P. S. and Links, J. (2013). Exactly solvable BCS-BEC crossover Hamiltonians. The XXIX International Colloquium on Group-Theoretical Methods in Physics, Tianjin, China, 20-26 August 2012. Hackensack, NJ, United States: World Scientific. doi: 10.1142/9789814518550_0018
Worsley, Susan, Bracken, Anthony, Hibberd, Katrina and Isaac, Phillip (2009). Introducing a group research project into a second-level mathematics course. UniServe Science Conference 2009, Sydney, NSW, Australia, 30 September - 2 October 2009. Sydney, NSW, Australia: UniServe Science.
Wagner, L., Links, J. and Isaac, P. (2005). Ribbon structure in symmetric pre-monoidal categories. XXV International Colloquium on Group Theoretical Methods in, Cocoyoc, Mexico, 2-6 August, 2004. Bristol, U.K.: Institute of Physics Publishing.
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.
Thesis
Isaac, Phillip S. (2001). Quasi Hopf superalgebras and their dual structures. PhD Thesis, School of Physical Sciences, The University of Queensland. doi: 10.14264/uql.2019.664