**CRM Proceedings & Lecture Notes**

Volume: 34;
2004;
227 pp;
Softcover

MSC: Primary 22; 81;

**Print ISBN: 978-0-8218-3409-1
Product Code: CRMP/34**

List Price: $98.00

AMS Member Price: $78.40

MAA Member Price: $88.20

**Electronic ISBN: 978-1-4704-3948-4
Product Code: CRMP/34.E**

List Price: $92.00

AMS Member Price: $73.60

MAA Member Price: $82.80

# Symmetry in Physics: In Memory of Robert T. Sharp

Share this page *Edited by *
*P. Winternitz; J. Harnad; C. S. Lam; J. Patera*

A co-publication of the AMS and Centre de Recherches Mathématiques

Papers in this volume are based on the Workshop on Symmetries in
Physics held at the Centre de recherches mathématiques (University of
Montreal) in memory of Robert T. Sharp. Contributed articles are on a variety
of topics revolving around the theme of symmetry in physics.

The preface presents a biographical and scientific retrospect of the life
and work of Robert Sharp. Other articles in the volume represent his diverse
range of interests, including representation theoretic methods for Lie
algebras, quantization techniques and foundational considerations, modular
group invariants and applications to conformal models, various physical models
and equations, geometric calculations with symmetries, and pedagogical methods
for developing spatio-temporal intuition.

The book is suitable for graduate students and researchers interested in
group theoretic methods, symmetries, and mathematical physics.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Readership

Graduate students and research mathematicians interested in applications of group theory in physics.

# Table of Contents

## Symmetry in Physics: In Memory of Robert T. Sharp

- Cover Cover11
- Frontispiece ii3
- Title page iii4
- Contents v6
- Preface vii8
- Bob Sharp: The man and the scientist ix10
- Bob Sharp: Teacher, colleague, friend xiii14
- Publications of Robert T. Sharp xvii18
- Participants xxiii24
- Symmetries and currents of massless neutrino fields, electromagnetic and graviton fields 126
- Naturalness and quintessence 1338
- Congruence subgroups of PSL(2,ℤ) 2348
- Asymptotic SU(2) and SU(3) Wigner functions from the weight diagram 3156
- Physical applications of a five-dimensional metric formulation of Galilean invariance 4368
- Variations on Dedekind’s eta 5580
- Examples of Berezin-Toeplitz quantization: Finite sets and unit interval 6792
- A modified Weierstrass representation for CMC-surfaces in multi-dimensional Euclidean spaces 77102
- Boson realizations of semi-simple Lie algebras 87112
- Stretched Littlewood-Richardson and Kostka coefficients 99124
- Group actions on compact hyperbolic manifolds and closed geodesics 113138
- Is there an ultimate symmetry in physics? 125150
- Formal characters and resolution of infinite-dimensional simple 𝐴ᵣ-modules of finite degree 131156
- Fusion rules and the Patera-Sharp generating-function method 141166
- Transient effects in Wigner distribution phase space of a scattering problem 153178
- R. T. Sharp and generating functions in group theory 159184
- Quasi-exact solvability in nonlinear optics 165190
- Coherent states, induced representations, geometric quantization, and their vector coherent state extensions 177202
- Symmetry math video game used to train profound spatial-temporal reasoning abilities equivalent to dynamical knot theory 189214
- Polytope sums and Lie characters 203228
- Subalgebras of Lie algebras. Example of sl(3,ℝ) 215240
- Back Cover Back Cover1256