韩国裸舞

Instanton calculus in quantum mechanics: Feynman diagrams and divergent series.

In this talk we discuss quantum mechanical problems, the double-well and sine-Gordon potentials, for which perturbation theory fails to explain physical properties even qualitatively. We then explain how non-perturbative effects can be obtained by instanton calculus. The corresponding Feynman diagrams (integrals) are used for the calculation of the tunneling amplitude up to the three-loop order. Unlike the two-loop contribution where all involved Feynman integrals are rational numbers, we will show that in the three-loop case they contain irrational contributions as well.