3 Non-Fock Representations

Franco Strocchi

Kozo Koizumi, Ikuo S. Sogami

Eigenfunctions of the Fock and non-Fock irreducible representations are explicitly derived for the q-deformed oscillators of the Macfarlane and Dubna types. While the Fock representations are composed of localized functions, the non-Fock representations consist of nonlocal oscillating functions which are constructed for the first time in this paper. The concept of the q-Hermite functions is generalized to include both the Fock and non-Fock types in a unified manner.

Franco Strocchi

Franco Strocchi

As anticipated in the previous discussions, the Fock representation is very special to the finite-dimensional case and to free fields. Actually, as a consequence of Proposition 12.1 , non-Fock representationsNon-Fock representation are required in order to describe many-particle systems with non-zero density in the thermodynamical limit.

Franco Strocchi

Mich�le Irac-Astaud, Guy Rideau