INTEGRAL REPRESENTATIONS OF THE SCHR¨ ODINGER PROPAGATOR

2 2m 1 + V (x), where V is a potential function modeling one-particle scattering p roblems. By means of a strongly converging regularization of the Schrodinger propagator U(t), we introduce a new class of integral representations for the relaxed kernel in terms of oscillatory integrals. They are constructed with complex amplitudes and real phase functions that belong to the class of global weakly quadratic generating functions of the Lagrangian submanifolds 3 t ⊂ T ⋆ R n ×T ⋆ R n related to the group of classical canonical transformations φ t . Moreover, as a particular generating function, we consider the action functional A(γ ) = R t 0 1 m | ˙ γ (s)| 2 − V (γ (s)) ds evaluated on