By S. Albeverio, P. Combe, R. Hscogh-Krohn, G. Rideau, M. Sirugue-Collin, M. Sirugue, R. Stora

**Read or Download Feynman Path Integrals: Proceedings of the International Colloquium Held in Marseille, May 1978 PDF**

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**Extra info for Feynman Path Integrals: Proceedings of the International Colloquium Held in Marseille, May 1978**

**Example text**

And defining then~for f Po2 - A m(P)2 Y(P) , p2+l P = (Po' ~)' One v e r i f i e s where Po R(B)c D Y l ' Y2 E D, Ac (yi,Y2) = P f dP° ~l (p) (Po 2 - m(~)2)-Z ~2 (p) ( p 2 + l ) 2 dp RS i. ^YZ (p) ~ (PJ - m(p)2) + f ~s+l with P the principal value d i s t r i b u t i o n measurable function, we see t h a t ( [ Z ] ) ( H , Hence the normalized Entegral defined and we have for all c In p a r t i c u l a r , IA C e wi th i n 2 j ,k g (y) d y . 2) and c(~) an a r b i t r a r y non negative D, B, A ) is a Fresnel fourtuple.

19] [14] , [2 0 , []~ U n f o r t u n a t e l y , f o r a p p l i c a t i o n s to quantum mechanical problems, the functions to be i n t e g r a t e d being of the form f(y) = exp(W(y)), not as powerful as might be expected from the f i n i t e In f a c t our space F(H) for W is d i f f i c u l t to be extended preserving the discussion of the asymptotic expansion in powers of is replaced by -~ Iyl 2 Tr(A~