Quantum physics IV

PHYS-426 / 6 credits

Teacher(s): Carleo Giuseppe, Rossi Riccardo

Language: English

Summary

Introduction to the path integral formulation of quantum mechanics. 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 instantons.

Content

1. Path Integral formalism

  • Introduction
  • Propagators and Green's functions.
  • Quantum mechanics in imaginary time and statistical mechanics.

2. Perturbation theory

  • Green's functions: definition and general properties
  • Functional methods
  • Perturbation theory by Feynman diagrams

3. Semiclassical approximation

  • The semiclassical limit

4. Non perturbative effects

  • Reflection and tunneling through a barrier
  • Instantons

5. Interaction with external magnetic field

  • Gauge invariance in quantum mechanics
  • Aharonov-Bohm effect
  • Dirac's magnetic monopole and charge quantization.

Keywords

Path integral formalism. Green's function. Determinants. Feynman diagram. Feynman rules. Perturbation theory. Non-perturbative effects. Tunnelling. Instantons. Gauge-invariance. 

Learning Prerequisites

Recommended courses

Quantum physics I and II

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

Office hours Yes
Assistants Yes
Forum Yes

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

Notes/Handbook

 

 

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum physics IV
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum physics IV
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum physics IV
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum physics IV
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum physics IV
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Quantum physics IV
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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