Dr Phillip Isaac

Senior Lecturer

Mathematics

+61 7 336 53267

psi@maths.uq.edu.au

Priestley Building (67), Room 743

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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.

Featured projects	Duration
Non-semisimple Lie algebras
Star quasi Hopf algebras
Co-quasi Hopf algebras
Characteristic identities of Lie algebras
Lie symmetries of differential equations
Dirac-Dunkl operators and superintegrable systems

Publications

Journal Articles (36)

Conference Papers (5)

Thesis (1)

Journal Articles

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) ARTN 505202, 505202. 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 U_q[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

Areas of research

Mathematical education

Mathematical physics