PATH INTEGRALS ON A COMPACT MANIFOLD WITH NON-NEGATIVE CURVATURE
PATH INTEGRALS ON A COMPACT MANIFOLD WITH NON-NEGATIVE CURVATURE
A typical path integral on a manifold, $M$ is an informal expression of the form \frac{1}{Z}\int_{\sigma \in H(M)} f(\sigma) e^{-E(\sigma)}\mathcal{D}\sigma, \nonumber where $H(M)$ is a Hilbert manifold of paths with energy $E(\sigma) < \infty$, $f$ is a real valued function on $H(M)$, $\mathcal{D}\sigma$ is a \textquotedblleft Lebesgue measure \textquotedblright and …