Dr Phillip Isaac is a mathematician who is interested in studying the algebraic structures underlying integrable models in statistical mechancs and other applications in physics.
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 compiling the initial version of the lecture workbook for MATH1051.
His current research activities involve finding solutions of the Yang-Baxter equation related to finite group algebras, associated integrable models and Bethe ansatz approach. He also maintains a healthy interest in the stucture and representation theory of Lie algebras, quantum groups, Quasi Hopf algebras, twisting (in the sense of Drinfeld) and other generalised algebraic structures.
Recently he has become interested in developing mathematical models of detonation theory, and more generally the study of travelling waves and their stability.
Journal Article: A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras
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: . doi:10.1088/1751-8121/aaa468
Journal Article: Reduced Wigner coefficients for Lie superalgebra gl(m|n) corresponding to unitary representations and beyond
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: . doi:10.1088/1751-8121/aa8119
Journal Article: Two-site Bose-Hubbard model with nonlinear tunneling: classical and quantum analysis
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: . doi:10.1103/PhysRevA.95.043607
Unified theory of Richardson-Gaudin integrability
(2015–2017) ARC Discovery Projects
Constructive representation theory of classical and quantum Lie superalgebras
(2014–2016) ARC Discovery Projects
Mathematics of anyonic models.
(2008–2009) UQ Early Career Researcher
On the construction of Casimir operators for non-semisimple Lie algebras
Doctor Philosophy
A pattern calculus for lie superalgebras
Doctor Philosophy
Analysis of the exact solution for the p+ip pairing Hamiltonian
Doctor Philosophy
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: . 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: . doi:10.1088/1751-8121/aa8119
Two-site Bose-Hubbard model with nonlinear tunneling: classical and quantum analysis
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: . doi:10.1103/PhysRevA.95.043607
An integrable case of the p + ip pairing Hamiltonian interacting with its environment
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: . doi:10.1088/1751-8113/49/8/084001
Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)
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: 121703-1-121703-19. doi:10.1063/1.4938076
Reduced matrix elements of the orthosymplectic Lie superalgebra
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: 1-39. doi:10.1088/1751-8113/48/2/025201
On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system
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
On realizations of polynomial algebras with three generators via deformed oscillator algebras
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: 1-26. doi:10.1088/1751-8113/47/20/205203
Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
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: 011703.1-011703.32. doi:10.1063/1.4861706
Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)
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: . 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: 1250118.1-1250118.25. doi:10.1142/S0129167X12501182
A variational approach for the quantum inverse scattering method
Andrew Birrell, Isaac, Phillip and Links, Jon R. (2012) A variational approach for the quantum inverse scattering method. Inverse Problems, 28 3: 035008.1-035008.15. doi:10.1088/0266-5611/28/3/035008
BEC-BCS crossover in a (p + ip)-wave pairing Hamiltonian coupled to bosonic molecular pairs
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
On irreducible representations of the exotic conformal Galilei algebra
Aizawa, N and Isaac, PS (2011) On irreducible representations of the exotic conformal Galilei algebra. Journal of Physics A-Mathematical and Theoretical, 44 3: 1-8. doi:10.1088/1751-8113/44/3/035401
Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D-3) symmetry
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
Integrable boundary conditions for a non-Abelian anyon chain with D(D3) symmetry
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
Assessment of an innovative system of lecture notes in first-year mathematics
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
Universal Baxterization for Z-graded Hopf algebras
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
An algebraic approach to symmetric pre-monoidal statistics
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: 103511-1-103511-18. doi:10.1063/1.2359575
Weak Hopf algebras corresponding to U-q[sl(n)]
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
Casimir invariants from quasi-Hopf (super)algebras
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
Characteristic identities for Lie (super)algebras
Isaac, Phillip S., Werry, Jason L. and Gould, Mark D. (2015). Characteristic identities for Lie (super)algebras. In: 30th International Colloquium on Group Theoretical Methods in Physics (Group30), Ghent Belgium, (012045.1-012045.10). 14-18 July, 2014. doi:10.1088/1742-6596/597/1/012045
Introducing a group research project into a second-level mathematics course
Worsley, Susan, Bracken, Anthony, Hibberd, Katrina and Isaac, Phillip (2009). Introducing a group research project into a second-level mathematics course. In: 2009 Conference Proceedings. UniServe Science Conference 2009, Sydney, NSW, Australia, (125-131). 30 September - 2 October 2009.
Ribbon structure in symmetric pre-monoidal categories
Wagner, L., Links, J. and Isaac, P. (2005). Ribbon structure in symmetric pre-monoidal categories. In: G. S. Pogosyan, L. E. Vicent and K. B. Wolf, Group Theoretical Methods in Physics. XXV International Colloquium on Group Theoretical Methods in, Cocoyoc, Mexico, (557-562). 2-6 August, 2004.
Quasi-Lie algebras and a method for determining non-degeneracy of the quasi-Lie product
Gould, MD and Isaac, PS (1998). Quasi-Lie algebras and a method for determining non-degeneracy of the quasi-Lie product. In: Group 22: Proceedings of the Xii International Colloquium On Group Theoretical Methods in Physics. 12th International Colloquium on Group Theoretical Methods in Physics (Group 22), Hobart Australia, (418-422). Jul 13-17, 1998.
Quasi Hopf superalgebras and their dual structures
Isaac, P. (2000). Quasi Hopf superalgebras and their dual structures PhD Thesis, School of Physical Sciences, The University of Queensland.
Unified theory of Richardson-Gaudin integrability
(2015–2017) ARC Discovery Projects
Constructive representation theory of classical and quantum Lie superalgebras
(2014–2016) ARC Discovery Projects
Mathematics of anyonic models.
(2008–2009) UQ Early Career Researcher
On the construction of Casimir operators for non-semisimple Lie algebras
Doctor Philosophy — Principal Advisor
Other advisors:
A pattern calculus for lie superalgebras
Doctor Philosophy — Principal Advisor
Other advisors:
Analysis of the exact solution for the p+ip pairing Hamiltonian
Doctor Philosophy — Associate Advisor
Other advisors:
Richardson-Gaudin models from the Boundary Quantum Inverse Scattering Method
(2016) Doctor Philosophy — Associate Advisor
Other advisors:
Unitary Representation Theory of the Lie Superalgebra gl(m|n)
(2015) Doctor Philosophy — Associate Advisor
Other advisors:
Aspects of Quantum Phase Space
(2012) Doctor Philosophy — Associate Advisor
Solutions to the Yang-Baxter equation and the Drinfield double of group algebras
(2010) Doctor Philosophy — Associate Advisor
Other advisors:
Spectra of Transfer Matrices of Exactly Solvable Models with D(D3) Symmetry
(2010) Doctor Philosophy — Associate Advisor
Other advisors:
On the Construction of Braided Pre-monoidal Nonassociative Categories
(2008) Doctor Philosophy — Associate Advisor
Other advisors: