Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2001; 38(2): 297-309

Printed March 1, 2001

Copyright © The Korean Mathematical Society.

Coherent state representation and unitarity condition in white noise calculus

Nobuaki Obata

Nagoya University

Abstract

White noise distribution theory over the complex Gaussian space is established on the basis of the recently developed white noise operator theory. Unitarity condition for a white noise operator is discussed by means of the operator symbol and complex Gaussian integration. Concerning the overcompleteness of the exponential vectors, a coherent state representation of a white noise function is uniquely specified from the diagonal coherent state representation of the associated multiplication operator.

Keywords: white noise, coherent state representation, Fock space, quantum stochastic differential equation, unitarity condition, operator symbol

MSC numbers: Primary: 60H40; Secondary: 46F25, 46A32, 46L53, 81S25