Duality Induced Reflections and CPT

TL;DR

This paper explores how fundamental symmetries like charge conjugation, parity, and time reversal can be derived from the selfduality of certain mathematical group representations related to particles and spacetime.

Contribution

It demonstrates that C, P, and T symmetries are induced by the selfduality of representations of groups associated with spin, Lorentz transformations, and time translations.

Findings

C, P, T symmetries are inducible by selfduality of specific group representations.

Linear CP-reflection for quarks is impossible due to non-equivalence of SU(3) triplet and antitriplet representations.

The approach links fundamental symmetries to the mathematical structure of group representations.

Abstract

The linear particle-antiparticle conjugation $\ty C$ and position space reflection $\ty P$ as well as the antilinear time reflection $\ty T$ are shown to be inducable by the selfduality of representations for the operation groups $\SU(2)$, $\SL(\C^2)$ and $\R$ for spin, Lorentz transformations and time translations resp. The definition of a colour compatible linear $\ty{CP}$-reflection for quarks as selfduality induced is impossible since triplet and antitriplet $\SU(3)$-representations are not linearly equivalent.