Field Theory and Many Body Physics 1
B. de Wit, 15 x 90 minutes,
Fall 2000
Classes: Thursday 11:00-13:00, BBL 105b
Tutorials: Thursday 13:15-17:00, BBL 165/166a
This course is offered as part of the international master's programme in theoretical physics
First lecture: Thursday 14 September
First tutorial: Thursday 14 September
Last lecture: Thursday, to be announced
Last tutorial: Thursday, to be announced
Written exam: Thursday 18 January
Tutorials leader: N.A.J. Obers (Spinoza 407,
tel 2969).
Assistents:
Jürg Käppeli (Spinoza
408, tel 5926),
Ivo Savonije (Spinoza 414, tel
2958)
(This web page is preliminary)
Contents
The lectures aim at giving a first introduction to
quantum field
theory as it is used in particle physics and in condensed matter
physics, without to much emphasis on specific applications, starting
from ordinary quantum mechanics. Ideally, after this course, students
shoudl take a more specialized course in field theoretic approaches to
elementary particle physics and/or condensed matter physics.
The quantization of field theories is treated in both the canonical
formalism and by means of path integrals. The main features are often
elucidated in systems with a finite degrees of freedom. Topics
discussed are the quantum-mechanical treatment of systems with an
infinite number of degrees of freedom, correlation functions and
generating functionals, field theories at finite temperature, tunneling
described in terms of instantons and quantization of fermions.
Perturbation theory is defined in terms of Feynman diagrams through
the path-integral representation. The diagrammatic description also
covers items such as the Dyson equation for Green's functions. Quantum
electrodynamics is introduced as a simple example of a gauge theory.
Literature:
Lecture notes: B. de Wit, Introduction to Quantum Field Theory
Book: B. de Wit and J. Smith, Field Theory in Particle Physics,
North-Holland Physics Publ. 1986.
Schedule
L: Lecture notes B: Book Lecture 1 (14 September): L1 Path integrals and quantum mechanics L2 The classical limit Exercises: 1.1, 2.1, 2.2, 2.3 Lecture 2 (21 September): L2 The classical limit B1.2 The Lagrangian for continuous systems Exercises: 2.4, 2.8, 2.5, 2.6 Lecture 3 (28 September): L3 Field theory Exercises: 3.1, 3.3, 3.4, 3.5 Lecture 4 (5 October): L4 Correlation functions Exercises: 4.1, 3.2, 3.8 Lecture 5 (12 October): L4 Correlation functions L5 Euclidean theory Exercises: 4.2, 4.3, 3.6, 5.1, 5.2 Lecture 6 (19 October): L5 Euclidean theory L7 Perturbation theory Exercises: 4.5, 5.2, 5.4, 5.5 Lecture 7 (26 October): L7 Perturbation theory B2.4 Feynman rules for spinless fields Exercises: 7.1, 7.3, B2.2, B2.3, 7.5 Lecture 8 (2 November): B2.5 An example: pion-pion scattering B2.6 Quantum corrections Exercises: B2.3, B2.4, B2.5, 7.8 Lecture 9 (9 November): L6 Tunneling and instantons Exercises: 7.8, 7.5, 7.6, 6.1 Lecture 10 (16 November): L6 Tunneling and instantons Exercises: 6.2, 7.7, 7.9 Lecture 11 (23 November): L9 Fermionic harmonic oscillators L10 Anti-commuting c-numbers Exercises: 5.7, 6.3, 6.4, 9.1, 9.2 Lecture 12 (30 November): L11 Phase space with commuting and anticommuting coordinates and quantization Exercises: 6.5, 9.3, 9.4, 11.2 Lecture 13 (7 December): L12 Path integrals for fermions B4.1 Massive spin-1 particles Exercises: 10.3, 11.1, 11.3, 12.1 Lecture 14 (14 December): B4.2 Massless spin-1 particles B5.1 Feynman rules for spin-1/2 fields B5.2 Lagrangians for fermions: (b) Quantum electrodynamics Exercises: 11.3, 12.2, 12.3, B4.5 Lecture 15 (21 December): L13 Regularization and Renormalization Exercises: 12.4, 13.1, 13.2, 13.5
last update: 20/12/2000.