Chapter

Symmetries II: Discrete spacetime symmetries

Anthony Duncan

in The Conceptual Framework of Quantum Field Theory

Published in print August 2012 | ISBN: 9780199573264
Published online January 2013 | e-ISBN: 9780191743313 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199573264.003.0013
Symmetries II: Discrete spacetime symmetries

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This chapter shows that the combination of these three discrete operations — parity, time reversal, and charge conjugation — is an exact symmetry of any local relativistic quantum field theory, even when none of the individual operations represents an exact symmetry of the theory. This result — commonly referred to as the TCP theorem — is first obtained for the case of theories with a dynamics specified by a Lagrangian (or Hamiltonian) density; and secondly, in a more general framework, by appealing to the irreducible fundamental properties of local field theory as incorporated in the Wightman axioms of Section 9.2. As a natural concomitant of the axiomatic proof of the TCP theorem, the chapter also indicates how the Spin-Statistics connection arises from the spectral and locality axioms of the Wightman formulation of field theory, with no commitment needed to a specific Lagrangian/Hamiltonian dynamics.

Keywords: parity; time reversal; charge conjugation; symmetry; relativistic quantum field theory; TCP theorem; Spin-Statistics theorem

Chapter.  10210 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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