This course covers the concepts and physical pictures behind various phenomena that appear in interacting many-body systems. Visualization occurs through concentration on path integral, mean-field theories and semi-classical picture of fluctuations around mean-field state.

Syllabus

Description

This course covers the concepts and physical pictures behind various phenomena that appear in interacting quantum many-body systems. Key ideas/techniques to be covered include broken symmetry, effective field theories, functional integral methods, and quantum phase transition theory.

A rough syllabus is:

• Second quantization; path integrals in quantum mechanics
• Interacting bosons - superfluidity
• Broken symmetry and its consequences
• Low dimensional quantum magnetism

Prerequisites

Quantum Physics II (8.05), Statistical Physics II (8.08), Relativity (8.033) or Classical Mechanics II (8.21), Physics of Solids I (8.231)

Homework

There will typically be one homework every week which will be due on the same day of the following week. Late homework is strongly discouraged!!

Presentation

There will be no final exam - instead there will be a short in-class presentation on a topic of general interest to the material in the course. Specific recommendations for presentation topics will be provided later.

Books

No single textbook will be used. What follows is a list of books that I find useful. When appropriate, lecture notes or references to review articles/research papers will be provided.

Negele, John W., and Henri Orland. Quantum Many-Particle Systems. Boulder, CO: Westview Press, October 1998. ISBN: 9780738200521.

Stone, Michael. The Physics of Quantum Fields. New York, NY: Springer-Verlag, February 1999. ISBN: 9780387989099.

Auerbach, Assa. Interacting Electrons and Quantum Magnetism. New York, NY: Springer-Verlag, 1994. ISBN: 9780387942865.

Wen, Xiao-Gang. Quantum Field Theory Of Many-body Systems: From The Origin Of Sound To An Origin Of Light And Electrons. Oxford, UK; New York, NY: Oxford University Press, 2004. ISBN: 9780198530947.

Sachdev, Subir. Quantum Phase Transitions. Cambridge, UK; New York, NY: Cambridge University Press, 2000. ISBN: 9780521582544.

Anderson, P. W. Basic Notions of Condensed Matter Physics. Boulder, CO: Westview Press, November 27, 1997. ISBN: 9780201328301.

Fradkin, Eduardo. Field Theories of Condensed Matter Systems. Boulder, CO: Westview Press, August 26, 1998. ISBN: 9780201328592.

Polyakov, A. M. Gauge Fields and Strings. New York, NY: Harwood Academic Publishers, Taylor & Francis Scientific, Technical and Medical, October 1, 1987. ISBN: 9783718603930.