Introduction to Many Body Physics.

620 Fall 2015

Piers Coleman, Rutgers University.
First day of class: Weds Sept 9th 2015.

Images Monograph Texts
Times of Course
Syllabus outline


Maxwellian construction of a Fermi Surface

Cuprate superconductor levitating a magnet.

Quantum Critical Point:
"Black hole" in the material phase diagram.

Adiabatic concept: basis of perturbation theory.

(Return to top)

Instructor: Piers Coleman, Room 268
If you have any enquiries about this course or the homework, please do not hesitate to contact me via email at : coleman@physics.rutgers.edu

Scope of Course. Many body physics provides the framework for understanding the collective behavior of vast assemblies of interacting particles. This course provides an introduction to this field, introducing you to the main techniques and concepts, aiming to give you first-hand experience in calculations and problem solving using these methods.

Students with disabilities 

    Introduction to Many Body Physics.

          The content of this course, with additional material will be published in 2015 by Cambridge
University Press.  I regret that the course material is no longer available for download, but will be available for purchase by November 2015.  Attendees of the class will be provided copies of the chapters we study.

Introduction to Many Body Physics


(Return to top)

  • Texts: The main reference text will be
      ``Many-Particle Physics'', Third Edition  by G. Mahan. (Plenum).
    but I  shall be basically teaching from my monograph.   Here are some other good references:


      • Condensed Matter Field Theory by Alexander Altland and Ben Simons.(CUP, 2006)
        An excellent introduction to Field Theory applied in condensed matter physics. I almost decided to make this the main text, as I like it greatly. 
      • Basic Notions in Condensed Matter Physics by P. W. Anderson. A classic reference. Many of us still turn to this book for inspiration, and philosophy. It also has a fine selection of important reprints at the back.

      Traditional Many Body Theory and Greens Functions

      • ``Methods of Quantum Field Theory in Statistical Physics'' by Abrikosov, Gorkov and Dzyalozinskii. (Dover Paperback) - Classic text from the sixties, known usually as AGD.
      • ``A guide to Feynman Diagrams in the Many-Body problem by R. D. Mattuck. A light introduction to the subject. Reprinted by Dover.
      • ``Greens functions for Solid State Physics'' S.Doniach and E. H. Sondheimer. Not as thorough as AGD, but less threatening and somehow more manageable. Frontiers in Physics series no 44.
      • ``Quantum Many Particle Systems'' by J. W. Negele and H. Orland. Alas all the good physics is in the unsolved excercises! However, it is the only one of this set to touch on the subject of functional integrals.

      Newer approaches to Many-Body Problem.

      • R. Shankar, Rev Mod Phys 66 129 (1994). An amazingly self-contained review of the renormalization group and functional integral techniques written by one of the best expositors of condensed matter physics.
      • ``Field Theories of Condensed Matter Physics'' by E. Fradkin. (Frontiers in Physics, Addison Wesley). Interesting material on the fractional statistics and the fractional quantum Hall effect.
      • ``Quantum Field Theory in Condensed Matter Physics'' by A. Tsvelik. (Cambridge paper back) Very good for one dimensional systems. No exercises.

      Further references:

      • The Theory of Quantum Liquids by D. Pines and P. Nozieres. Excellent introduction to Fermi liquid theory that avoids the use of field theory.
      • Statistical Physics, vol II by Lifshitz and Pitaevskii. Pergammon. Marvellous book on applications of many body physics, mainly to condensed matter physics.

      Online references     (Check it out- this is a great link).

(Return to top)

Exercises 620
(Return to top)

          Initial quiz 
          Exercise 1 (2015)   Solutions
          Exercise 2 (2015)

(Return to top)        Note: this material is copywritten and should not be posted without permission.

Times: 12.00 am on Wednesday  and 1.40 pm on Fridays in  ARC-212. We will start one week late, due do my travel, on Wednesday,  September 9th. Quite frequently, to make up for my travel, we will hold an additional  class. This will take place at 10.20am in ARC 205 most Mondays. I apologize for this inconvenience.

Office hour:   9.50 Fridays or by arrangement.  Tel x 5082.

Assessment:   Assessment will be made on the basis of weekly assignments, a take-home mid-term and a take-home final exam. I want to encourage an interactive class and will take this into account when grading!

(Return to top)

  We will make a selected sortie through the following list. Asterisks indicate areas that will be high priority

  • Second Quantization. ``Free'' systems-- the building block of the quasiparticle concept. *
  • Phonons and photons, Fermi and Bose fluids; spin-systems (x-y) model. Interactions.*
  • Green's Functions and Feynman diagrams .*
  • Finite temperature Green Functions.  *
  • Application of Finite temperature  Feynman Diagrams to (i) electron-phonon problem * ; (ii) transport theory.
  • Functional Integral Approach (if time permits).
  • Broken Symmetry and Superconductivity.  *

(Return to top)



Make-up class
Mon:  10.20pm 
ARC 205

Weds 12:00
ARC 212

Fri 1:40pm
ARC 212

1. Aug 31-Sep 4

No Classes This Week No Class
No Class

2 Sept 7-11
No Class Fields overview.
Einsteins phonon: the Simple Harmonic Oscillator
Collective Quantum Fields: 1 and 3D

3 Sept 14-18
Collective Quantum Fields: continuum and thermodynamic limit. Conserved Particles:
Canonical Commutation Rules

4 Sep 21-Sept 25
No Class No Class
No Class

5 Sept 28-Oct 2
Particles in thermal equilibrium. Examples of 2nd Quantization
Jordan Wigner Transformation, 1D Ferromagnet.
Examples of 2nd Quantization
1 D Antiferromagnet. Hubbard Model

6 Oct 5-  9
No Class Examples of 2nd Quantization
Free Bosons, Fermions
Greens functions:
Interaction rep/Driven Oscillator

7. Oct 12- 16
Greens Functions:
Free Fermions and Bosons
Catch up and review.
Adiabaticity  I
Gell-Mann Low Theorem

8. Oct 19 - 23
Adiabaticity  II
Landau Fermi
Liquid Theory
Adiabaticity  II
Landau Fermi
Liquid Theory
Feynman diagrams:
Heuristic derivation

9. Oct 26 -30
Feynman Rules
Linked Cluster Theorem
No Class
No Class

10.  Nov 2 -  6
Linked Cluster Theorem. Electron in scattering potential. Hartree Fock. Response functions. Lindhard Function. RPA Approach.
Large N electron gas

11.  Nov 9- 13
Finite T
Imaginary time   Green functions
Finite T
Feynman Rules and examples
Finite T
Feynman Rules:
Electron in a disordered potential

12.  Nov 16 - 20
No Classes
No Classes
No Classes

13. Nov 23 - Nov 27
Finite T:
Electron Phonon
interaction: self energy; Migdal's theorem.
Note: Friday Schedule. Meet 1.40pm. Superconductivity:
No class- Thanksgiving

14.  Nov 30 - Dec 4
Superconductivity   BCS Theory I Superconductivity   BCS Theory II  Nambu Green functions.

15.  Dec 7 -Dec 11
The Meissner Effect
Wrap up.

(Return to top)