Q-space Representation of Boson Fock Space

John Edward Gough, Joachim Kupsch

Uwe Franz, Nicolas Privault

Un-Cig Ji, Young-Yi Kim

A Fock representation of q-commutation relation is studied by constructing a q-Fock space as the space of the representation, the q-creation and q-annihilation operators (-1 < q < 1). In the case of 0 < q < 1, the q-Fock space is interpolated between the Boson Fock space and the full Fock space. Also, a unitary decomposition of the q-Fock space $(q\;{\neq}\;0)$ is studied.

Paul Lee Robinson

We detail a new approach to the bosonic Fock representation of a complex Hilbert space V: our account places the bosonic Fock space S[V] between the symmetric algebra SV and its full antidual SV'; in addition to providing a context in which arbitrary (not necessarily restricted) real symplectic automorphisms of V are implemented, it offers simplified proofs of many standard results of the theory.