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)
Topics:
Quantization through path integrals
Equivalence of the path integral formulation and “ordinary” Quantum Mechanics: states, operators, wave function, Schrödinger equation
Euclidean formulation; Green's functions; spectral representation
Saddle point method; vacuum tunneling and instantons
Perturbation theory
Fermions trough path integrals: Grassman variables
Discretization of the path integrals and lattice artifacts; improved actions; boundary conditions
Introduction to the Monte-Carlo methods
Topological effects: Aharonov-Bohm effect, Dirac monopole and charge quantization; particle statistics; anyons
Path integral in the holomorphic representation; quantization of a scalar field; perturbation theory; generating functional
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
Script:
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 8: Path integral in QFT
Lecture 9: Quantization of the gauge fields