PHYS-426 / 6 credits

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.

Keywords

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

Recommended courses

Quantum physics I, II and III

Quantum Field Theory I

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.

Written exam

Supervision

 Office hours Yes Assistants Yes Forum Yes

Bibliography

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

"Techniques and applications of Path Integration'',  L.S. Schulman, John Wiley & Sons Inc., 1981.

"Path Integral Methods and Applications", R. MacKenzie, arXiv:quant-ph/0004090.

"Modern Quantum Mechanics'',  J.J. Sakurai, The Benjamin/Cummings Publishing Company, 1985.

"Aspects of Symmetry", S.  Coleman, Cambridge University Press, 1985.

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

Notes/Handbook

Lecture Notes for Quantum Mechanics IV

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

Reference week

 Mo Tu We Th Fr 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

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