Department for General and Applied Physics, Moscow Institute of Physics and Technology

Chair for "Problems in theoretical physics"

based at Landau Institute for theoretical physics


Asymptotic methods of complex analysis

K.S. Tikhonov


  1. Asymptotic series.
    • Asymptotic series: introduction and motivation.
    • Borel summation.
    • Asymptotic evaluation of integrals.
    • Hyperasymptotics and resurgence.
  2. Examples from Quantum Mechanics and theory of Ordinary Differential Equations.
    • WKB approximation, turning points and Stokes geometry for linear ODEs.
    • Phase integral methods in non-stationary, scattering and eigenvalue problems.
    • Anharmonic Oscillator.
    • Nonlinear connection problems.
  3. Examples from Quantum Field Theory.
    • Effective action and derivative expansion.
    • Analytic continuation of path integrals.
    • Path integrals with multiple zero modes.
    • Complex saddle points in path integrals.

Course details