2016/08/18 by Andreas Trautner, Trautner, Andreas · 1 citation
Physics and Astronomy · #Atomic and Subatomic Physics Research #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Neutrino Physics Research #Other Condensed Matter (cond-mat.other) #Particle physics theoretical and experimental studies
paper · pdf · doi:10.48550/arxiv.1608.05240
openalex publication_date 2016/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer automorphisms is pedagogically introduced and it is shown that CP transformations are special outer automorphisms of the global, local, and space-time symmetries of a theory. It is shown that certain discrete groups allow for a group theoretical prediction of parameter independent CP violating complex phases with fixed geometrical values. The remainder of this thesis pioneers the study of outer automorphisms which are not related to C, P, or T. It is shown how outer automorphisms, in general, relate symmetry invariants and, in theories with spontaneous symmetry breaking, imply relations between different vacuum expectation values. Thereby, outer automorphisms can give rise to emergent symmetries. An example model with a discrete symmetry and three copies of the Standard Model Higgs field is discussed, in which the rich outer automorphism structure completely fixes the Higgs VEVs in their field space direction, including CP violating relative phases. This underlies the phenomenon of spontaneous geometrical CP violation. The possible relevance of outer automorphisms for a wide field of future studies is highlighted.