On a $q$-Fock Space and Its Unitary Decomposition
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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 ($q\ne0$) is studied.
Abstract
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 ($q\ne0$) is studied.
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