Quantum physics IV
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
- Path Integrals in Quantum Mechanics / Zinn-Justin
- Path integrals in quantum mechanics, statistics, polymer physics, and financial markets / Kleiner
- Quantum Mechanics and Path Integrals / Feynman & Hibbs
Notes/Handbook
Moodle Link
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Quantum physics IV
- Courses: 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
- Courses: 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
- Courses: 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
- Courses: 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
- Courses: 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
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional