Unitary group representations in Fock spaces with generalized exchange properties (Q1900500)

Canonical commutation relations (CCR) form the basis of second quantization. There are instances where \(q\)-deformed CCR play an important role. In the present note the authors suggest to study \(R\)- deformed CCR, where \(R(x,y)\) is a complex-valued function on \(\mathbb{R}^s \times \mathbb{R}^s\): \[ a(x) a(y) - R(x,y) a(y) a(x) = \delta (x - y). \] The Fock representations of these relations are described. Central to this work is the \(R\)-quantization of operators, i.e., the way in which unitary operators \(V\) on the one-particle space are (functorially) extended to unitary operators on the entire Fock space. The claim, that the developed formalism is well adapted to deal with the problems of anyon field theory, has not been substantiated in a convincing manner.