A Proof of the Gutzwiller Semiclassical Trace Formula Using Coherent States Decomposition

Abstract:The Gutzwiller trace formula links the eigenvalues of the Schrödinger operator as Planck's constant goes to zero (the semiclassical régime) with the closed orbits of the corresponding classical mechanical system. Gutzwiller gave a heuristic proof of this trace formula, using the Feynman integral representation for the propagator of . Later, using the theory of Fourier integral operators, mathematicians gave rigorous proofs of the formula in various settings. Here we show how the use of coherent states allows us to give a simple and direct proof.