Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics

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.

References in corpus (1)

• Semigroup Representations of the Poincare Group and Relativistic Gamow Vectors

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