A Spin-Statistics Theorem for Quantum Fieldson Curved Spacetime Manifoldsin a Generally Covariant Framework
Abstract
A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic spacetimes will be given which generalizes similar, previous approaches. Here, a generally covariant quantum field theory is an assignment of quantum fields to globally hyperbolic spacetimes with spin-structure where each quantum field propagates on the spacetime to which it is assigned. Imposing very natural conditions such as local general covariance, existence of a causal dynamical law, fixed spinor- or tensor type for all quantum fields of the theory, and that the quantum field on Minkowski spacetime satisfies the usual conditions, it will be shown that a spin-statistics theorem holds: If for some of the spacetimes the corresponding quantum field obeys the ``wrong'' connection between spin and statistics, then all quantum fields of the theory, on each spacetime, are trivial.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- 2001
- DOI:
- 10.1007/s002200100526
- arXiv:
- arXiv:math-ph/0102035
- Bibcode:
- 2001CMaPh.223..261V
- Keywords:
-
- Mathematical Physics;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Mathematics - Mathematical Physics
- E-Print:
- latex2e, 1 figure, 32 pages