The Current Galilei Algebra and Associated Random Variables

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New Zealand Journal of Mathematics

Vol. 41, (2011), Pages 131-142


Luigi Accardi

Centro Vito Volterra,

Universita di Roma Tor Vergata

via Columbia 2, 00133 Roma, Italy

mailto:accardi@volterra.mat.uniroma2.it

Andreas Boukas

Centro Vito Volterra,

Universita di Roma Tor Vergata

via Columbia 2, 00133 Roma, Italy

mailto:andreasboukas@yahoo.com




Abstract We compute the Fock kernel for the one-mode (i.e. restricted to a single interval) and current (i.e. extended to simple functions) Galilei algebra. We also compute the characteristic function of a family of random variables naturally associated with the Galilei algebra.

Keywords Galilei algebra, Heisenberg algebra, Central extension, Fock representation, Fock kernel, Renormalized Higher Powers of White Noise

Classification (MSC2000) Primary 17B15, 17B56, 60B15, 81S05. Secondary 81R05, 81S25.

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