Introduction to path integrals - a short course for PhD students
Academic year 2017-2018
Course description
The path integral approach is a key tool in modern physics. In this course you will learn the basics of the technique of path integration and a set of connections and applications of this approach. You will explore how the path integral approach of quantum mechanics gives a profound understanding of the relation between quantum and classical mechanics. You will learn how the path integrals reveal a deep relation between quantum field theory and statistical physics of phase transitions. You will learn how to extend this approach to many-body systems.
This course is addressed to beginning PhD students in condensed matter and particle physics. The only prerequisite of this course is an undergraduate knowledge of quantum and statistical mechanics.
Syllabus
Path integrals in quantum mechanics; path integrals and phase transitions; path integrals and many-body physics.
Times/Location
Autumn Term 2017, Tuesdays 14:00 - 15:00; Room: T125; 12 hours of lectures
Suggested readings
- L. S. Shulman, Techniques and Applications of Path Integration, Dover (2005)
- Jean Zinn-Justin, Path Integrals in Quantum Mechanics, Oxford University Press (2013)
- R. P. Feynman, A. R. Hibbs, Quantum Mechanics and Path Integrals, Dover (2010)
Lecture topics
Tuesday 26 September 2017:
I. Path integrals in quantum mechanics; I.1. Path integral formulation of quantum mechanics; I.1.a Double-slit experiment; I.1.b Intuitive approach to path integral
Tuesday 03 October 2017:
I.1.c From Schrödinger equation to path integral; I.1.c.i Evolution operator; I.1.c.ii Propagator
Tuesday 10 October 2017:
I.1.c.iii Propagator as a functional integral; I.1.d Application: free particle
Tuesday 17 October 2017:
I.1.e Application: harmonic oscillator; II.1.e.i Path integral for the harmonic oscillator
Tuesday 24 October 2017:
II.1.e.i Path integral for the harmonic oscillator (continue); II.1.e.ii Physical interpretation
Tuesday 31 October 2017:
II.1.e.ii Physical interpretation (continue); II. Path integrals and phase transitions; II.1. Path integral and statistical mechanics; II.1.a Euclidean propagator; II.1.b Partition function as a path integral
Tuesday 7 November 2017:
II.1.c Partition function of the harmonic oscillator; II.1.d Partition function of the harmonic oscillator: classical limit
Tuesday 14 November 2017:
III. Path intragrals and phase transitions. III.1. Ising model.
Tuesday 21 November 2017:
III.2. Ising model: mean-field theory.
Tuesday 28 November 2017:
III.2. Ising model: mean-field theory (continue).
Tuesday 5 December 2017:
No lecture.
Tuesday 12 December 2017:
III.3. Ising model and path integral.