Double Symmetries in Field Theories

TL;DR

This paper introduces the concept of double symmetry in field theories, providing definitions, construction methods, and an example, while discussing implications for weak interaction symmetries and P-violation.

Contribution

It presents a new concept of double symmetry, offers two construction methods for double-symmetric theories, and analyzes the dual role of certain symmetry groups in weak interactions.

Findings

High efficiency of one construction method demonstrated

Dual status of $SU(2)_L \otimes SU(2)_R$ group analyzed

Implications for P-violation in weak interactions discussed

Abstract

In the paper a concept of a double symmetry is introduced, and its qualitative characteristics and rigorous definitions are given. We describe two ways to construct the double-symmetric field theories and present an example demonstrating the high efficiency of one of them. In noting the existing double-symmetric theories we draw attention at a dual status of the group $SU(2)_{L} \otimes SU(2)_{R}$ as a secondary symmetry group, and in this connexion we briefly discuss logically possible aspects of the $P$-violation in weak interactions.