On the one-mode quadratic Weyl operators

Xian-Ting Liang

Jian-ming Du, Jian-guo Ma, Gang Ren

Luigi Accardi, Habib Ouerdiane, Habib Rebei

In this paper we introduce the quadratic Weyl operators canonically associated to the one mode renormalized square of white noise (RSWN) algebra as unitary operator acting on the one mode interacting Fock space {Γ, {ωn, n ∈ ℕ}, Φ} where {ωn, n ∈ ℕ} is the principal Jacobi sequence of the nonstandard (i.e. neither Gaussian nor Poisson) Meixner classes. We deduce the quadratic Weyl relations and construct the quadratic analogue of the Heisenberg Lie group with one degree of freedom. In particular, we determine the manifold structure of the group and introduce a local chart containing the identity on which the group law has a simple rational expression in the chart coordinates (see Theorem 6.3).

C. L. Mehta

The Weyl ordered form of the operator exp[αâ2+βâ2++γ (â+â+ââ+)] is derived in a very simple way. Using this result, we also obtain the normal and antinormal ordered forms as well as the diagonal coherent states representation of this operator.

Leon W. Cohen

RL Hudson, Kalyanapuram Rangachari Parthasarathy