STOCHASTIC WESS-ZUMINO-WITTEN MODEL OVER A SYMPLECTIC MANIFOLD

Over the path space of a symplectic manifold with end points in two La grangian submanifolds, we define a measure and a stochastic symplectic action in the simply connected case. We define a regularized Wess-Zum ino-Witten Laplacian over the forms of finite degree over the path spa ce. We perform a short time asymptotic near the critical points and fi nd a limit Brownian harmonic oscillator: we can diagonalize it explici tly, and find the limit ground state of the Laplacian. We define a sto chastic Witten complex, and its algebraic counterpart at the level of Chen forms.