Representation of Semigroups in Rigged Hilbert Spaces: Subsemigroups of the Weyl-Heisenberg Group

TL;DR

This paper explores how differentiable representations of specific subsemigroups of the Weyl-Heisenberg group can be constructed within rigged Hilbert spaces, linking group representations to quantum mechanics frameworks.

Contribution

It introduces a method to obtain differentiable semigroup representations from unitary group representations in rigged Hilbert spaces, with applications to time asymmetric quantum mechanics.

Findings

Representation construction in rigged Hilbert spaces demonstrated

Connections to time asymmetric quantum mechanics established

Framework for subsemigroup representations developed

Abstract

This paper studies how differentiable representations of certain subsemigroups of the Weyl-Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary representation of the Weyl-Heisenberg group in a Hilbert space. Aspects of the rigged Hilbert space formulation of time asymmetric quantum mechanics are also investigated within the context of the results developed here.