Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics

Research paper by S. Wickramasekara, A. Bohm

Indexed on: 08 Feb '03Published on: 08 Feb '03Published in: Mathematical Physics

Abstract

We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space.