## Web Access Research Portal

# Researcher: Jarvis, PD (Dr Peter Jarvis)

## Fields of Research

Physical Sciences

Biological Mathematics

Particle Physics

Algebraic Structures in Mathematical Physics

Group Theory and Generalisations

Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory

Integrable Systems (Classical and Quantum)

Mathematical Aspects of Quantum and Conformal Field Theory, Quantum Gravity and String Theory

Phylogeny and Comparative Analysis

Mathematical Physics

Condensed Matter Characterisation Technique Development

Optimisation

Mathematical Aspects of General Relativity

German Language

Biological Physics

Quantum Physics

Gene Expression (incl. Microarray and other genome-wide approaches)

Approximation Theory and Asymptotic Methods

Operations Research

Nuclear Physics

Molecular Evolution

Genetic Immunology

Statistical Theory

Stochastic Analysis and Modelling

Atomic, Molecular, Nuclear, Particle and Plasma Physics

Medical Biotechnology

Applied Statistics

Theoretical and Computational Chemistry

## Research Objectives

Expanding Knowledge in the Physical Sciences

Expanding Knowledge in the Mathematical Sciences

Expanding Knowledge in the Biological Sciences

Expanding Knowledge in the Environmental Sciences

Expanding Knowledge in Philosophy and Religious Studies

Communication Equipment

Flora, Fauna and Biodiversity at Regional or Larger Scales

## Career Best Publications

A Hopf laboratory for symmetric functions; **Journal of Physics A-Mathematical and General**

A supersymmetric model for the evolution of the genetic code; **Proceedings of the National Academy of Sciences of the United States of America**

Adventures in invariant theory; **ANZIAM Journal**

Extended BRS invariance and OSp (4/2) supersymmetry; **Journal of Physics A: General Physics**

Extended two-level quantum dissipative system from bosonization of the elliptic spin-½ Kondo model; **Journal of Physics A: Mathematical and Theoretical**

Hidden supersymmetry-a 'no superpartner' theorem for representations of deformed conformal superalgebra; **Journal of Physics A: Mathematical and Theoretical**

Low-parameter phylogenetic inference under the general Markov model; **Systematic Biology**

Markov invariants, plethysms, and phylogenetics; **Journal of Theoretical Biology**

New branching rules induced by plethysm; **Journal of Physics A: Mathematical and General**

Path integral formulation and Feynman rules for phylogenetic branching models; **Journal of Physics A: Mathematical and General**

Resolution of the *GL*(3) *O*(3) state labelling problem via the *O*(3)-invariant Bethe subalgebra of the twisted Yangain; **Journal of Physics A: Mathematical and General**

The mixed two qutrit system: local unitary invariants, entanglement monotones, and the SLOCC group SL(3,C); **Journal of Physics A**

The mixed two-qubit system and the structure of its ring of local invariants; **Journal of Physics A: Mathematical and Theoretical**

## Research Publications

A Base-Pairing Model of Duplex Formation. I. Watson-Crick Pairing Geometries; **Biopolymers**

A class of quadratic deformations of Lie superalgebras; **Journal of Physics A: Mathematical and Theoretical**

A generalised Baker-Campbell-Hausdorff formula with application to coset space parameterisation; **Physics Letters A**

A Hopf algebraic approach to the theory of group branchings; **Symmetry, Spectroscopy and SCHUR**

A Hopf laboratory for symmetric functions; **Journal of Physics A-Mathematical and General**

A kinematical approach to gravitational lensing using new formulae for refractive index and acceleration; **Monthly Notices of the Royal Astronomical Society**

A representation-theoretic approach to the calculation of evolutionary distance in bacteria; **Journal of Physics A: Mathematical and Theoretical**

A supersymmetric model for the evolution of the genetic code; **Proceedings of the National Academy of Sciences of the United States of America**

A tensorial approach to the inversion of group-based phylogenetic models; **BMC Evolutionary Biology**

Adventures in invariant theory; **ANZIAM Journal**

Algebraic inversion of the Dirac equation for the vector potential in the non-Abelian case; **Journal of Physics A: Mathematical and Theoretical**

An Algebraic Model of RNA Duplex Formation; **Biopolymers**

Axial anomalies by dimensional reduction; **Journal of Physics G: Nuclear Physics**

Axial anomalies in higher dimensions by dimensional continuation; **Journal of Physics G: Nuclear Physics**

Born Reciprocity and the Granularity of Spacetime; **Foundations of Physics Letters**

Born Reciprocity in Two Dimensions: Quaplectic Group Symmetry, Branching Rules and State Labelling; **The Proceedings of the Festschrift in Honor of Bruce JH McKellar and Girish C Joshi**

Bridging the World

Chord Diagrams and BPHZ Subtractions; **Modern Physics Letters A**

Codon and nucleotide assignments in a supersymmetric model of the genetic code; **Physics Letters A**

Concise Encyclopedia of Supersymmetry and noncommutative structures in mathematics and physics; **Kluwer Academic Publishers**

Conformal fluid dynamics; **Nuclear Physics B**

Constrained O(*n*) models from gauged internal OSp(^{n}/_{2}) via Becchi-Rouet-Stora supersymmetry; **Physical Review D**

Constraint quantization of a worldline system invariant under reciprocal relativity: II; **Journal of Physics A: Mathematical and Theoretical**

Covariance, correlation and entanglement; **Journal of Physics A-Mathematical and General**

Covariant scalar representation of iosp(d,2/2) and quantization of the scalar relativistic particle; **Journal of Physics A**

Covariant spinor representation of *iosp(d*, 2/2) and quantization of the spinning relativistic particle; **Journal of Physics A-Mathematical and General**

Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov invariants; **Journal of Mathematical Biology**

Dimensional reduction and axial anomalies; **Journal of Physics G: Nuclear Physics**

Entanglement invariants and phylogenetic branching; **Journal of Mathematical Biology**

Erratum-Entanglement invariants and phylogenetic branching; **Journal of Mathematical Biology**

Exactly solvable three-level quantum dissipative systems via bosonization of fermion gas-impurity models; **Journal of Physics A : Mathematical and Theoretical**

Exotic Gauge Potential Representations and Ghost Counting Via Orthosymplectic Brs Supersymmetry; **Journal of Physics A: Mathematical and General**

Extended Becchi-Rouet-Stora invariance for gravity via local OSp(^{4}/_{2}) supersymmetry; **Physical Review D**

Extended BRS invariance and OSp (4/2) supersymmetry; **Journal of Physics A: General Physics**

Extended two-level quantum dissipative system from bosonization of the elliptic spin-½ Kondo model; **Journal of Physics A: Mathematical and Theoretical**

Fierz bilinear formulation of the Maxwell-Dirac equations and symmetry reductions; **Annals of Physics**

Gauge fixing of stringlike models via OSp(D/2); **Modern Physics Letters A**

Generalized Characteristic Identities and Applications; **Confronting the Infinite**

Generalized scalar particle quantization in 1+1 dimensions and *D*(2,1;?); **Journal of Physics A: Mathematical and General**

Grassmann coordinates and Lie algebras for unified models; **Journal of Mathematical Physics**

Gravitational contribution to the chiral anomaly in higher dimensions; **Physics Letters B**

Hidden supersymmetry-a 'no superpartner' theorem for representations of deformed conformal superalgebra; **Journal of Physics A: Mathematical and Theoretical**

Hopf algebras and characters of classical groups; **Symmetry and Structural Properties of Condensed Matter**

Hopf algebras, distributive (Laplace) pairings and hash products: a unified approach to tensor product decompositions of group characters; **Journal of Physics A: Mathematical and Theoretical**

Integrity bases for local invariants of composite quantum systems; **Journal of Physics A: Mathematical and General**

Invariants of mixed qubit systems; **Symmetry, Spectroscopy and SCHUR**

Is the general time-reversible model bad for molecular phylogenetics?; **Systematic Biology**

Lie Markov models; **Journal of Theoretical Biology**

Lie Markov models with purine/pyrimidine symmetry; **Journal of Mathematical Biology**

Lie Super-Algebraisation of BRST-BFV Covariant Quantization; **Proceedings of the II International Workshop Lie Theory and Its Applications in Physics II**

Local OSp(4/2) supersymmetry and extended BRS transformations for gravity; **Physics Letters B**

Low-parameter phylogenetic inference under the general Markov model; **Systematic Biology**

Markov invariants and the isotropy subgroup of a quartet tree; **Journal of Theoretical Biology**

Markov Invariants for Phylogenetic Rate Matrices Derived from Embedded Submodels; **IEEE/ACM Transactions on Computational Biology and Bioinformatics**

Markov invariants, plethysms, and phylogenetics; **Journal of Theoretical Biology**

Matrix group structure and Markov invariants in the strand symmetric phylogenetic substitution model; **Journal of Mathematical Biology**

Matter fields and fermions in OSp(^{4}/_{2}) by dimensional reduction via supercoset space; **Physics Letters B**

Maximum likelihood estimates of pairwise rearrangement distances; **Journal of Theoretical Biology**

Maxwell-Dirac stress-energy tensor in terms of Fierz bilinear currents; **Annals of Physics**

Models for Fermion Generations Based on 5 Fermionic Coordinates; **Australian Journal of Physics**

Models for supersymmetric quantum-mechanics; **Australian Journal of Physics**

Modified relativity from the kappa-deformed Poincare algebra; **Classical and Quantum Gravity**

New branching rules induced by plethysm; **Journal of Physics A: Mathematical and General**

Off-shell kappa-symmetry of the superparticle and the spinning superparticle; **Physics Letters B**

On Associative Superalgebras of Matrices; **Rocky Mountain Journal of Mathematics**

On boson algebras as Hopf algebras; **Journal of Physics A**

On schizosymmetric superfields and *sl*(2/1, C)_{R} supersymmetry; **Journal of Physics A: Mathematical and General**

On the structure of the observable algebra of QCD on the lattice; **Journal of Physics A: Mathematical and General**

Path integral formulation and Feynman rules for phylogenetic branching models; **Journal of Physics A: Mathematical and General**

Phylogenetic Invariants; **Brenner's Encyclopedia of Genetics**

Phylogenetic Invariants and Markov Invariants; **Reference Module in Life Sciences**

Plethysms, replicated Schur functions and series, with applications to vertex operators; **Journal of Physics A:Mathematical and Theoretical **

Plethystic vertex operators and boson-fermion correspondences; **Journal of Physics A: Mathematical and Theoretical**

Polynomial super-*gl(n)* algebras; **Journal of Physics A: Mathematical and General**

Projective representations of the inhomogeneous Hamilton group: Noninertial symmetry in quantum mechanics; **Annals of Physics**

Quantised gauge theory, dimensional reduction and OSp(4+NM/2) supersymmetry; **Journal of Physics A: Mathematical and General**

Quantum deformations and *q*-boson operators; **Journal of Physics A: Mathematical and Theoretical**

Quantum field theory and phylogenetic branching; **Journal of Physics A: Mathematical and General**

Quantum Physics Meets Biology: a Case Study; **Preserving the Humboldt tradition of scholarship in Australia**

Realizations of Physical Particle States Via Cohomologies: Algebraization of BRST-BFV Covariant Quantization; **5th Wigner Symposium**

Regularized tripartite continuous variable EPR-type states with Wigner functions and CHSH violations; **Journal of Physics A: Mathematical and Theoretical**

Reports on Mathematical Physics; **Reports on Mathematical Physics**

Resolution of the *GL*(3) *O*(3) state labelling problem via the *O*(3)-invariant Bethe subalgebra of the twisted Yangain; **Journal of Physics A: Mathematical and General**

Review of article by Bougourzi, AH; Weston, RA entitled A free field representation of the screening currents of Uq(sl(3)); **Mathematical Reviews**

Review of article by Fuchs, J and Schweigert, C entitled Non-Hermitian symmetric N = 2 coset models, Poincare polynomials, and string compactification; **Mathematical Reviews**

Review of article by Gould, MD and Scheunert, M entitled Classification of finite-dimensional unitary irreps for Uq(gl(m/n)); **Mathematical Reviews**

Review of article by Mankoc-Borstnik, N entitled Spinors, vectors and scalars in Grassmann space and canonical quantization for fermions and bosons; **Mathematical Reviews**

Ribbon Hopf algebras from group character rings; **Linear and Multilinear Algebra**

Schizosymmetry - A new paradigm for superfield expansions; **Modern Physics Letters A**

Sp(2) Invariant BRST formalism, Supersymmetry and Wess-Zumino gauges; **Modern Physics Letters A**

Spectroscopy of the genetic code; **Quantum Aspects Of Life**

Supersymmetry in the Genetic Code; **XXI International Colloquium on Group Theoretical Methods in Physics**

Symmetric Functions, Tableaux Decompositions and the Fermion-Boson Correspondence; **Mathematical and Computer Modelling**

Symmetric Functions, Vertex Operators and Applications*; **Yamada Conference XL XX International Colloquium on Group Theoretical Methods in Physics**

Tensor rank, invariants, inequalities, and applications; **Journal on Matrix Analysis and Applications**

The Algebra of the General Markov Model on Phylogenetic Trees and Networks; **Bulletin of Mathematical Biology**

The Dirichlet Hopf Algebra of Arithmetics; **Journal of Knot Theory and Its Ramifications**

The genetic code as a periodic table: algebraic aspects; **Biosystems**

The Hopf algebra structure of the character rings of classical groups; **Journal of Physics A: Mathematical and Theoretical**

The mixed two qutrit system: local unitary invariants, entanglement monotones, and the SLOCC group SL(3,C); **Journal of Physics A**

The mixed two-qubit system and the structure of its ring of local invariants; **Journal of Physics A: Mathematical and Theoretical**

The molecular asymmetric rigid rotor Hamiltonian as an exactly solvable model; **Molecular Physics**

Tunnelling of a Molecule; **Australian Journal of Physics**

U(1) × U(1) × U(1) symmetry of the Kimura 3ST model and phylogenetic branching processes; **Journal of Physics A-Mathematical and General**

Using the tangle: A consistent construction of phylogenetic distance matrices for quartets; **Mathematical Biosciences**

World-line quantization of a reciprocally invariant system; **Journal of Physics A: Mathematical and Theoretical**

## Research Projects

Algebraic Aspects of Renormalization; **Australian Research Council (ARC)**

Algebraic Aspects of the Genetic Code; **University of Tasmania (UTAS)**

Algebraic Structures in Mathematical Physics and their Applications; **Australian Research Council (ARC)**

Algebraically informed models of biological sequence evolution; **Australian Research Council (ARC)**

DNA-Protein Binding: Dependence of Binding Rate upon Local DNA Flexibility; **University of Tasmania (UTAS)**

Grassmann variables and unified models; **Australian Research Council (ARC)**

Infinite-Dimensional Algebras and Field Theory Applications; **Australian Research Council (ARC)**

Markov Invariants and Phylogenetic Tree Reconstruction; **Australian Research Council (ARC)**

Spacetime supersymmetries and particle classification; **Australian Research Council (ARC)**

Structure and Informatics of the Genetic Code; **Australian Research Council (ARC)**

Structure of the genetic code; **Australian Research Council (ARC)**

XXII ICGTMP - Group 22; **Australian Agency for International Development (AusAID)**

## Research Candidate Supervision

A Kinematical Approach to Gravitational Lensing

A Modern Approach to Born Reciprocity

A Scattering Approach to Gravitational Lensing

An investigation of the Jacobson radical of epigroup graded rings

Characterising and Investigating the Semigroup Generated by Three-Arched Diagrams

Classical and Quantum non-linear supersymmetries biology

Clifford Algebras and Geometry of Entanglement

Entanglement and the Quantum-classical Transition

Entanglement, Invariants, and Phylogenetics

Group Invariant Solutions of the Yang-Mills Equations for Weak and Electroweak Interactions

Infinite -dimensional algebras in Mathematics and Physics

Multidimensional Phase Space

Nonlinear Superalgebras and Lattice Gauge Theory

On Group Invariant Solutions to the Maxwell Dirac Equations

Structural and Combinatorial Aspects of Graded Rings with Applications

Superalgebraisation of BFV-BRST Quantisation

The SuperHiggs Mechanism for Anticommuting Coordinates

Theoretical Physics

Universal Couplings in two body stong and electromagnetic Meson decays