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.