TRANSFORMATIONS OF FEYNMAN-INTEGRALS UNDER NONLINEAR TRANSFORMATIONS OF THE PHASE-SPACE

The Feynman measure is defined as a linear continuous functional on a test-function space (introduced in the paper). The functional is given by means of its Fourier transform. Not only a positive-definite corre lation operator but also one without fixed sign is considered (the lat ter case corresponds to the so-called symplectic, or Hamiltonian, Feyn man measure). The Feynman integral is the value of the Feynman measure on a function (ire the test-function space). The effect on the Feynma n measure of nonlinear transformations of the phase space in the form of shifts along vector fields or along integral curves of vector field s is described. Analogs of the well-known Cameron--Martin, Girsanov-Ma ruyama, and Ramer formulas in the theory of Gaussian measures are obta ined. The results of the paper can be regarded as,formulas for a chang e of variable in Feynman integrals.