Generalized Fock spaces and second quantization as examples of
In my talk we will consider the following topics:
- Generalized Fock spaces F(T,H) for real contraction T on a real Hilbert space H.
- Anyonic Fock spaces and q-CCR relations for |q|=1 and connections with type B-Fock spaces.
- Second quantization Γ(T,S) from the von Neumann algebra G(T,H) generalized by T-Gaussian operators G(f) = a(f) + a+(f), where f is in a real Hilbert space H.
- If S = exp(-t) Id, we get so called generalized Ornstein-Uhlenbeck semigroup
Ut = Γ(T,S) and in many cases of T we have ultrarcontactivity, i.e.
Ut maps L2 into L∞ , where here L2 = the Fock space F(T,H) and
L∞ = G(T,H).
The subject of the talk is taken from the main results of the papers together with W. Ejsmont, T. Hasebe, E. Lytvynov, I. Rodionova, Q. Xu and J. Wysoczański.
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