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Proof of the TCP Theorem

✍ Scribed by Gerhart Lüders

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 122 KB
Volume: 281
Category: Article
ISSN: 0003-4916
DOI: 10.1006/aphy.2000.6027

No coin nor oath required. For personal study only.

✦ Synopsis

A comparatively simple proof is given for the general theorem that a wide class of quantized field theories which are invariant under the proper Lorentz group is also invariant with respect to the product of time reversal (T), charge conjugation (C), and parity (P). In the proof use is made of an important simplification introduced by Pauli.

1957 Academic Press

I. DEFINITION OF THE OPERATIONS 1. Interaction Representation

Since we want to present a proof of the theorem which is not restricted to interactions without derivatives of the field operators, we employ the interaction representation. In this representation the field operators obey equations of motion without interaction and free field commutation relations. We list these equations for the various types of fields we will be using. 2

Spin 0: (g 2 &m 2 ) .(x)=0, (g 2 &m 2 ) .*(x)=0 (I.1.1) [.*(x), .(x$)]=&i2(x&x$), [.(x), .(x$)]=[.*(x), .*(x$)]=0; (I.1.2) Spin 1: (g 2 &m 2 ) . + (x)=0, (g 2 &m 2 ) . + *(x)=0, (I.1.3) + . + (x)=0, + . + *(x)=0, (I.1.4

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