Derivation of the TCP Theorem using Action Principles

TL;DR

This paper introduces a new, more fundamental derivation of the TCP/CPT Theorem using Action Principles, extending its applicability to complex quantum systems with interactions, bound states, and unstable states.

Contribution

It provides a novel proof of the TCP/CPT Theorem based on the invariance of the Variation of Action, removing previous constraints related to free fields and asymptotic conditions.

Findings

New proof extends TCP/CPT applicability to complex systems

Proof based on invariance of Action with interactions included

Applicable to bound states and unstable states

Abstract

We present a new derivation of the proof for the TCP/CPT Theorem using the Dynamical Principle and Variation of Action methods first defined by Schwinger in 1951. This new proof will significantly extend the TCP Theorem beyond the original proofs by Pauli-Luders and Jost, which were significantly constrained by limits of free quantum fields and the asymptotic condition. This paper gives a more fundamental proof based on invariance of the Variation of Action with interactions included and no free field or asymptotic condition on the quantum fields. This new proof for TCP/CPT can now be applied to more complicated quantum field systems that include n-particle bound states and unstable states.