We study the propagation of coherent states in self-interacting bosonic quantum field theories in the semi-classical (mean-field) regime. Our work focuses in particular on the spatially cutoff P(\phi)_2 model, under standard assumptions ensuring essential self-adjointness of the Hamiltonian. For this model, the classical field equation is given by a non-linear Klein-Gordon equation, whose well-posedness constitutes the first step of our analysis. We then apply Hepp’s method, combined with a detailed study of both the classical and quantum dynamics, in order to construct an asymptotic expansion of arbitrary order for the quantum evolution of coherent states.

The comparison between analytic and topological torsion of a smooth compact manifold equipped with a unitary flat vector bundle,  aka Cheeger-Müller theorem, is one of the most important comparison theorems in global analysis. Refined versions of both analytic and topological torsion on a smooth compact manifold have been amply studied as well.

The aim of this talk is to present extensions of the Cheeger-Müller theorem for torsion as well as for refined torsion on singular spaces with conical singularities.