Introduction to path integrals

Lecturer: Akaki Rusetsky (University of Bonn)


Regional Training Center in Theoretical Physics

Lectures: On February 16,18,20,23,25,27 at 16:00 in room 220

Prerequisits: Quantum Mechanics, elements of Quantum Field Theory (desirable)



  1. Quantization through path integrals

  2. Equivalence of the path integral formulation and “ordinary” Quantum Mechanics: states, operators, wave function, Schrödinger equation

  3. Euclidean formulation; Green's functions; spectral representation

  4. Saddle point method; vacuum tunneling and instantons

  5. Perturbation theory

  6. Fermions trough path integrals: Grassman variables

  7. Discretization of the path integrals and lattice artifacts; improved actions; boundary conditions

  8. Introduction to the Monte-Carlo methods

  9. Topological effects: Aharonov-Bohm effect, Dirac monopole and charge quantization; particle statistics; anyons

  10. Path integral in the holomorphic representation; quantization of a scalar field; perturbation theory; generating functional

  11. Theories with constraints; quantization of the gauge fields

Not all topics can be covered in 6 lectures. In case of interest, the continuation of the lectures through videoconferencing is possible.

Recommended literature:


R.P. Feynman and A.R. Hibbs, Quantum Mechanics and path integrals.

L.D. Faddeev and A.A. Slavnov, Gauge fields: an introduction to quantum theory.

R. MacKenzie, Path integral methods and applications, arXiv:quant-ph/0004090

G.P. Lepage, Lattice QCD for novices, arXiv:hep-lat/0506036

M. Creutz and B. Freedman, A statistical approach to Quantum Mechanics, Ann. Phys. 132 (1982) 427

A. Khelashvili, Feynman's functional integral and some of its applications




Lecture 1: Fundamentals

Lecture 2: Euclidean path integral, Green's functions, spectral representation and all that

Lecture 3: Perturbation theory

Lecture 4: Vacuum tunneling and instantons

Lecture 5: Coherent states and path integrals

Lecture 6: Topological effects

Lecture 7: Numerical methods

Lecture 8: Path integral in QFT

Lecture 9: Quantization of the gauge fields