Laplace asymptotic expansions of conditional Wiener integrals and generalized Mehler kernel formulas
Ian M Davies, Aubrey Truman · Journal of Mathematical Physics · 1982
Imitating Schilder’s results for Wiener integrals rigorous Laplace asymptotic expansions are proven for conditional Wiener integrals. Applications are given for deriving generalized Mehler kernel formulas, up to arbitrarily high orders in powers of ℏ, for exp{−TH(ℏ)/ℏ}(x, y), T>0 where H(ℏ)=[(−ℏ2/2)Δ1+V], Δ1 being the one-dimensional Laplacian, V being a real-valued potential V∈C∞(R), bounded below, together with its second derivative.