The Transformations T , C P and C P T in the Presence of Vacuum Degeneracy

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Abstract
The purpose of this paper is to examine the way in which concept relating to the improper transformations CP and T may be affected by the existence of a degeneracy of the vacuum. Two types of degeneracy are considered, that associated with the topological classification of gauge fields in non-abelian gauge theory and that associated with spontaneous symmetry breaking, as first suggested by Nambu. In the first case, the occurrence of “strong CP-violation” is related to the behavior of the degenerate vacuum. In the second, the occurrence of the CP-violation in weak interactions may be so related. The possibility that the vacuum is not invariant under these transformations clouds the meaning of the transformations themselves so that much of the body of this paper is a review from a new viewpoint of the way in which P, T and C may be defined as “kinematically admissible transformations” that do not require any assumptions about invariance of the dynamics or of the vacuum. In §7 these definitions and the resulting properties of CP and T are used as a basis for conjecture about the way in which the physical fields will be affected by them and as a basis for speculation about the origin of weak CP-violation. Questions are raised, but not fully resolved, about the proof of the CPT theorem for non-abelian gauge theories, especially for the phenomenological aspects of the theory. It is suggested that the θ-vacuum is CP-invariant so that what is called “strong CP-violation” may actually be strong T-violation.

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