The Quantum Geometry of Spin and Statistics

Abstract

Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case we classify the corresponding possibilities for anyonic spin and statistics. We incorporate the underlying extended concept of symmetry into quantum field theory in a generalised path integral formulation capable of handling general braid statistics. For bosons and fermions the different path integrals and Feynman rules naturally emerge without introducing Grassmann variables. We also consider the anyonic example of quons and obtain the path integral counterpart to the usual canonical approach.

23 pages, LaTeX with AMS and XY-Pic macros, minor corrections and references added

References in corpus (2)

• Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
• Braided Quantum Field Theory

Cited by in corpus (10)

• Diffeomorphisms in group field theories
• Fractional and noncommutative spacetimes
• Three-dimensional Quantum Supergravity and Supersymmetric Spin Foam Models
• Three dimensional Loop Quantum Gravity: towards a self-gravitating Quantum Field Theory
• The Quantum Geometry of Supersymmetry and the Generalized Group Extension Problem
• The Pauli Exclusion Principle and SU(2) vs. SO(3) in Loop Quantum Gravity
• Translation-Invariant Noncommutative Gauge Theories, Matrix Modeling and Noncommutative Geometry
• How should we choose the boundary conditions in a simulation which could detect anyons in one and two dimensions?
• Quantum and Classical Phase Space: Separability and Entanglement
• Quantum spin coverings and statistics