We show that the Feinsilver‐Kocik‐Schott (FKS) kernel for the Schrödinger algebra is not positive definite. We show how the FKS Schrödinger kernel can be reduced to a positive definite one through a restriction of the defining parameters of the exponential vectors. We define the Fock space associated with the reduced FKS Schrödinger kernel. We compute the characteristic functions of quantum random variables naturally associated with the FKS Schrödinger kernel and expressed in terms of the renormalized higher powers of white noise (or RHPWN) Lie algebra generators.
Accardi, L., Boukas, A. (2009). Random variables and positive definite Kernels associates with the Schrodinger algebra. In Lie theory and its applications in physics: 8th International Workshop / Vladimir Dobrev, editor. (pp.126-137). New York : AIP [10.1063/1.3460158].
Random variables and positive definite Kernels associates with the Schrodinger algebra
ACCARDI, LUIGI;
2009-06-01
Abstract
We show that the Feinsilver‐Kocik‐Schott (FKS) kernel for the Schrödinger algebra is not positive definite. We show how the FKS Schrödinger kernel can be reduced to a positive definite one through a restriction of the defining parameters of the exponential vectors. We define the Fock space associated with the reduced FKS Schrödinger kernel. We compute the characteristic functions of quantum random variables naturally associated with the FKS Schrödinger kernel and expressed in terms of the renormalized higher powers of white noise (or RHPWN) Lie algebra generators.File | Dimensione | Formato | |
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