Quantum physics IV

Summary

Introduction to the path integral formulation of quantum mechanics. Gauge invariance. Derivation of the perturbation expansion of Green's functions in terms of Feynman diagrams. Several applications will be presented, including non-perturbative effects, such as tunneling and instanton

Content

Keywords

Path integral formalism. Green's function. Determinants. Feynman diagram. Feynman rules. Perturbation theory. Non-perturbative effects. Tunnelling. Instantons, Gauge Invariance, imaginary time, thermal density matrix, Landau levels; Aharonov-Bohm effect, Berry phase; correlation functions, Wick's theorem, Feynman diagrams, variational principle, mean-field theory; semiclassical approximation; Bohr-Sommerfeld quantization, magnetic monopoles, Van Vleck-Pauli-Morette propagator.

Learning Prerequisites

Required courses

Analytical Mechanics

Physics III (Electromagnetism)

Statistical physics

Mathematical methods (for SPH)

Quantum Physics I, II

Recommended courses

Quantum Physics III

Important concepts to start the course

Solid knowledge and practice of calculus (complex variable) and linear algebra

Learning Outcomes

By the end of the course, the student must be able to:

• Formulate a quantum mechanical problem in terms of a Path integral
• Compute gaussian path integral as determinants
• Express physical quantities in terms of the Green function
• Translate a Feynman diagram into a mathematical expression
• Compute a Feynman diagram
• Compute tunneling rates in simple quantum potentials
• Formulate the quantum theory of a particle interacting with an external electromagnetic field

Transversal skills

• Use a work methodology appropriate to the task.
• Set objectives and design an action plan to reach those objectives.

Teaching methods

Ex cathedra and exercises

Expected student activities

Participation in lectures. Solving problem sets during exercise hours. Critical study of the material.

Assessment methods

Written exam

Supervision

Resources

Bibliography

"Quantum Mechanics and Path Integrals" , R.P. Feynman and A.R. Hibbs, McGraw-Hill, 1965.

"Path Integrals in Quantum Mechanics, Statistics and Polymer Physics'', Hagen Kleinert, World Scientific, 1995.

"Path Integrals in Quantum Mechanics", Jean Zinn-Justin, Oxford Graduate Texts, 2010.

Ressources en bibliothèque

• Find the references at the Library

Notes/Handbook

Moodle Link

• https://go.epfl.ch/PHYS-426