Definite and Indefinite Unitary Time Representations for Hilbert and Non-Hilbert Spaces

TL;DR

This paper explores different time representations for stable, unstable, and ghost states in quantum systems, emphasizing the role of unitary groups and Hilbert spaces, and introduces a generalized framework for unstable particles as probability collectives.

Contribution

It introduces a novel approach to modeling unstable particles using higher-dimensional nonabelian probability groups, extending traditional Hilbert space representations.

Findings

Unstable particles modeled as probability collectives with U(n) groups

Distinct time representations for stable, unstable, and ghost states

Generalization of normalization from U(1) to U(n) groups

Abstract

Stable states (particles), ghosts and unstables states (particles) are discussed with respect to the time representations involved, their unitary groups and the induced Hilbert spaces. Unstable particles with their decay channels are treated as higher dimensional probability collectives with nonabelian probability groups U(n) generalizing the individual abelian U(1)-normalization for stable states (particles).