Decompositions of regular representations of the canonical commutation relations (Q1174621)

Summary: 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.