Characterizing Volume Forms
نویسندگان
چکیده
Old and new results for characterizing volume forms in functional integration. 1 The Wiener measure Defining volume forms on infinite dimensional spaces is a key problem in the theory of functional integration. The first volume form used in functional integration has been the Wiener measure. From the several equivalent definitions of the Wiener measure, we choose one [1] which can easily be extended for use in Feynman integrals. We recall the CameronMartin and Malliavin formulae because they are, respectively, integrated and infinitesimal formulae for changes of variable of integration which can be imposed on volume forms other than the Wiener measure. 1.1 Definition The Wiener measure γ on the space W of pointed continuous paths w on the time interval T = [0, 1] w : [0, 1] −→ R , w(0) = 0, can be characterized by the equation
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