Representations Of Commutation Relations Research Articles

Commuting Operators for Representations of Commutation Relations Defined by Dynamical Systems

In this article, using orbits of the dynamical system generated by the function F, operator representations of commutation relations XX* = F(X*X) and AB = BF(A) are studied and used to investigate commuting operators expressed using polynomials in A and B. Various conditions on the function F, defining the commutation relations, are derived for monomials and polynomials in operators A and B to commute. These conditions are further studied for dynamical systems generated by affine and q-deformed power functions, and for the β-shift dynamical system.

Representations of commutation relations in BRST quantization

It is shown that the asymptotic state space in the BRST quantization is a Krein space. The equivalence of the representations, which are realized by the asymptotic fields in such spaces, is proved.

Expansion in eigenfunctions of families of commuting operators and representations of commutation relations

Expansion in eigenfunctions of families of commuting operators and representations of commutation relations

Inequivalence of representations of commutation relations obtained by orthogonal transformations in field theory

It is shown that, except under very special conditions, orthogonal transformations on the field coordinates of a Bose-Einstein field cannot be represented as transformations in the Hilbert space of the boson field. The proof is restricted to rotations which are products of commuting rotations in two-dimensional subspaces.