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Introduction to Many Body Physics.

620 Fall 2011

Piers Coleman, Rutgers University
Images Monograph Texts
 Exercises
 Times of Course
 Syllabus outline
 Timetable
 



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.

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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 
 





    The evolving monograph.

          The content of this course, with additional material is being written up as a monograph. Feel free
to download the text of the course.

      pdf    twocolumn version

(Updated 2011-12-01 ).

Please do not hesitate to email me corrections and typos.
 


 

Note: this material is copywrited.
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  • 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:

      Overview

      • 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).

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Exercises 620 (Return to top)

          Initial quiz  Answers to initial quiz
          Exercise 1 (2011)   Answers to Exercise 1
          Exercise 2 (2011)   Answers to Exercise 2
          Exercise 3 (2011)   Answers to Exercise 3
          Exercise 4 (2010)   Answers to Exercise 4
          Exercise 5 (2010)   Answers to Exercise 5
          Exercise 6 (2010)

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


Times: 12.00 am on Wednesday  and 1.40 pm on Fridays in  ARC-212 starting Wednesday,  September 7th.
On some weeks, particularly when I am travelling, we will hold an alternate class at 3pm in the CMT reading
room on Mondays.

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!

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Outline  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.
  • Broken Symmetry and Superconductivity.  *
  • Local moments and Heavy Electron Physics



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         Provisional schedule:


Week

 Extra classes
Time/location to be decided
Weds 12:00 ARC 212
Fri 1:40pm ARC 212

2 Sept 5-9

Fields overview.
Einsteins phonon: the SHE.
Collective Quantum Fields: 1 and 3D

3 Sept 12-19
Collective quantum fields: continuum and thermodynamic limit. Conserved Particles:
Canonical Commutation Rules

4 Sept 19-23
 Interactions
Conserved Particles in Thermal equilibrium
Homework 1 due
 Examples of 2nd Quantization
Jordan Wigner Transformation 		Examples of 2nd Quantization
1 D Ferromagnet.

5 Sep 26-Sept 30
 No Class.
 Examples of 2nd Quantization
Hubbard Model.		 Examples of 2nd Quantization
Free Bosons; Free Fermions

6 Oct 3-7
Greens functions:
Interaction rep/Driven Oscillator 		No office hour or class
No office hour or class

7 Oct 10-  14
 Greens Functions:
Free Fermions and Bosons
 Adiabaticity concept I
  Gell-Mann LowTheorem
No office hour or class

8. Oct 17- 21
 Adiabaticity  II
Landau Fermi
Liquid Theory		 Adiabaticity  II
Landau Fermi
Liquid Theory 		T=0
Feynman diagrams:
Heuristic derivation

9 Oct 24 - 28
 No Class
 No Class
 T=0
Feynman Rules
Linked Cluster Theorem

10 Oct 31 -Nov 4
Electron in scattering potential. Hartree Fock.  Response functions. Lindhard Function. 

11 Nov 7 -  11

RPA Approach.
Large N electron gas


12 Nov 14- 18


No office hour or class

13 Nov 21 - 25
 Finite T
Imaginary time   Green functions

Renormalized Weds. Meet noon. ARC 212
  No class- Thanksgiving
No class- Thanksgiving

14 Nov 28- Dec 2
 Finite T
Feynman Rules and examples 		Finite T
Feynman Rules:
Electron in a disordered potential		 Finite T:
Electron Phonon
interaction: self energy; Migdal's theorem.

15 Dec 5 - Dec 9
  Superconductivity and  BCS Theory
Superconductivity and  BCS Theory
Nambu Green functions. BCS wavefunction


16 Dec 12 Dec 16
 The Meissner effect


 


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