Physically Relevant Representations

Franco Strocchi

Roberto Beneduci

We study two relevant characterizations of a commutative positive operator valued measure (POVM) F . The first one is a Choquet type of an integral representation. It introduces a measure ν on the space of the projection valued measures (PVMs) and describes F as an integral over this space. The second one represents a commutative POVM F as the randomization of a single PVM E by means of a Markov kernel μ . We show that one can be derived from the other. We also elaborate upon some previous results on Choquet’s representation of Markov kernels and find a functional relationship between ν and μ . Finally, we analyze some relevant particular cases and provide some physically relevant examples which include the unsharp position observables.

Henk Hoogland

The projective equivalence relation for representations of symmetry groups in quantum mechanics is refined to a so-called gauge equivalence relation. An example is given where this leads to a physically more relevant classification of elementary quantum mechanical systems. It is indicated how this idea might be applied to projective bundle .representations.

Satoru Yamamoto

Emilio d’Emilio, Luigi E. Picasso