QWN-EULER OPERATOR AND ASSOCIATED CAUCHY PROBLEM

Abstract

In this paper the quantum white noise (QWN)-Euler operator [Formula: see text] is defined as the sum [Formula: see text], where [Formula: see text] and N Q stand for appropriate QWN counterparts of the Gross Laplacian and the conservation operator, respectively. It is shown that [Formula: see text] has an integral representation in terms of the QWN-derivatives [Formula: see text] as a kind of functional integral acting on nuclear algebra of white noise operators. The solution of the Cauchy problem associated to the QWN-Euler operator is worked out in the basis of the QWN coordinate system.