# Quantum Symmetry

A special issue of *Symmetry* (ISSN 2073-8994).

Deadline for manuscript submissions: **closed (31 January 2011)** | Viewed by 50925

## Special Issue Editor

## Special Issue Information

Dear Colleagues,

- Physical states represented in Hilbert space rather than phase space.
- Quantum mechanics defines symmetries as mappings between physical states that preserve transition amplitudes. (As Wigner proved, these symmetries can be represented in Hilbert space by unitary and anti-unitary operators.)
- Quantum mechanics assigns complex numbers to these transition amplitudes.
- The algebra of observables in quantum mechanics is non-commutative.
- Quantum particles are indistinguishable.
- Composite quantum systems are not represented by a Cartesian product structure, but by a linear tensor structure.

Contributions are invited on all aspects of quantum symmetries. Those that involve foundational issues or the intersection of theoretical physics and pure mathematics are especially welcomed. Possible themes (not ranked in order preference) include:

- 2D Conformal Field Theory, Modular Invariance, Statistical Mechanics.
- Dualities in Quantum Theories.
- Mirror Symmetry in String Theory.
- Emergent Quantum Symmetries, Symmetry Breaking, Effective Field Theory, Renormalization Group.
- Hopf Algebras, Quantum Groups and Low Dimensional Physics.
- Quantum Geometry (including Non-Commutative Geometry).
- Spin-Statistics, Anyons, Fractional Quantum Hall Effect.
- Connections between Quantum Symmetries and Spacetime/Object Dimensionality.
- Quantum Symmetries in Computation.
- Relationship between Classical and Quantum Symmetries.

Dr. Dean Rickles

*Guest Editor*

## Keywords

- quantum symmetry
- S-duality
- symmetry breaking
- anyons
- braid group
- quantum groups
- conformal field theory
- modular invariance