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Deciphering the Algebraic CPT Theorem

Swanson, Noel (2018) Deciphering the Algebraic CPT Theorem. [Preprint]

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Abstract

The CPT theorem states that any causal, Lorentz-invariant, thermodynamically well-behaved quantum field theory must also be invariant under a reflection symmetry that reverses the direction of time (T), flips spatial parity (P), and conjugates charge (C). Although its physical basis remains obscure, CPT symmetry appears to be necessary in order to unify quantum mechanics with relativity. This paper attempts to decipher the physical reasoning behind proofs of the CPT theorem in algebraic quantum field theory. Ultimately, CPT symmetry is linked to a systematic reversal of the C*-algebraic Lie product that encodes the generating relationship between observables and symmetries. In any physically reasonable relativistic quantum field theory it is always possible to systematically reverse this generating relationship while preserving the dynamics, spectra, and localization properties of physical systems. Rather than the product of three separate reflections, CPT symmetry is revealed to be a single global reflection of the theory’s state space.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Swanson, Noelnswanson@udel.edu0000-0002-5950-3863
Additional Information: Changes from version 1: streamlined discussion section, clarified motivation for project, emphasized lemmas 1-3 and role of state space geometry in section 3, clarified distinction between represented and implemented symmetries, corrected typos.
Keywords: CPT Theorem, Symmetries, Quantum Field Theory, Relativity, Quantum Mechanics
Subjects: Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Noel Swanson
Date Deposited: 20 Jun 2019 18:15
Last Modified: 20 Jun 2019 18:15
Item ID: 16138
Subjects: Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Symmetries/Invariances
Date: 17 October 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16138

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