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

/ENG

Asymptotic methods of complex analysis

K.S. Tikhonov

Complex analysis-2

K.S. Tikhonov

Syllabus

  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