JournalsprimsVol. 26 , No. 6DOI 10.2977/prims/1195170574

Decompositions of Regular Representations of the Canonical Commutation Relations

  • Reinhard Schaflitzel

    TU München, Germany
Decompositions of Regular Representations of the Canonical Commutation Relations cover

Abstract

Every cyclic regular representation of the canonical commutation relations over any inner product space V can be decomposed into a direct integral of irreducible regular representations, where the fibers are representations over subspaces of V. An example using the so-called direct-product representations shows that generally the irreducible representations cannot be defined over the whole V. So we get a new type of decomposition having no equivalent in the decompositions of locally compact groups.