It has long been realized by microlocal analysts that an alternative, ´Euclidean-signature´ semi-classical ansatz for solutions to Schrödinger´s equation is much more natural, from a mathematical point of view, than the classical, physics textbook, W.K.B. ansatz, even though the latter has the conceptual advantage of emphasizing the classical correspondence principle. For technical reasons though this microlocal approach has seemed to be limited to quantum mechanical problems and not to be applicable to quantum field theories. In this seminar I will review this method and discuss an expansive, ongoing project with A. Marini (Yeshiva, L´Aquila) and R. Maitra (Wentworth I.T.) to extend these influential ideas to bosonic quantum field theories including \phip type scalar and Yang-Mills fields.
