Analysis Seminar

Speaker: Alfonso Gracia-Saz (Toronto)

"Bohr-Sommerfeld rules and the symbol of a function of an operator"

Time: 15:00

Room: MC 108

Weyl Quantization provides a correspondence between quantum observables (i.e. operators on a Hilbert space) and classical observables (i.e. ``symbols'' or smooth functions on a Poisson manifold) in the description of a physical system. Bohr-Sommerfeld rules are an asymptotic method to calculate the eigenvalues of an operator via its symbol. To develop Bohr-Sommerfeld rules for an operator, we first need to solve the following problem: given an operator A and a function f, what is the symbol of f(A) in terms of the symbol of A? I will explain the context of this problem and give a solution in the form of a combinatorial formula ``a la Feynmann'', which has other applications in quantum mechanics