Many-Particle Physics. PhD course 15 hp (7.5+7.5)


Any piece of solid material contains of the order of 1023 interacting particles. The effects from the interaction between this huge number of particles and how these are treated theoretically is the field of many-particle physics.

The formalism is cumbersome and the course is suited for students with theoretical ability and interest. The time is shared equally between the formalism itself and applications. Both zero-temperature and finite-temperature formalisms are treated.

The concepts of Greenís functions, self-energies and correlation functions are dealt with and the students are taught to draw and interpret Feynman diagrams. Examples of applications: the electron gas, exchange- and correlation- effects, vacuum fluctuations, van der Waals and Casimir forces, mean-free-path, transport- versus life-time, the polaron, band-gap renormalization in bulk semiconductors and in quantum wells, current drag.
 

The examination is in the form of homework problems and an oral presentation.


We find in the course that the dielectric function is a very important quantity and determines many of the properties of the systems. Another course, TFYY70 Fundamentals of Surface Modes, is strongly recommended.  It covers a variety of  effects resulting from Maxwell's equations and the dielectric function..  Several of the results we derive in the many-particle course we may derive here in a much simpler way. Many of these effects appear in our every day life and many are utilized in several different branches of industry and in modern research. They are important on the border line between physics and biology, chemistry and medicine. Some key words: surface energy, surface tension, van der Waals force, Casimir force, vacuum fluctuations.
 
 



LECTURE NOTES
Introduction Homework Problems
Chap. 1 Formulas
Chap. 2
Chap. 3
Chap. 4
Chap. 5
Chap. 6
References










 


Literature

I will follow the book Many-Particle Physics  2nd or 3rd editions by G.D. Mahan (Plenum New York 1990 or 2000 ).
The first part, the basic theory part, will follow the book rather closely. In the second part, the application part, the applications are choosen differently.
 
 

Bo E. Sernelius, examiner
Room: G408
Phone: (+46) (0)13 28724
Fax: (+46) (0)13 137568
Email: bos@ifm.liu.se


PRELIMINARY SCHEDULE
Fö. 1  03-11-14 at 9.15 in Mott, Introduction
Fö. 2  03-11-21, Harmonic Oscillator and Phonons
Fö. 3  03-11-28, Second Quantization for Particles
Fö. 4  03-12-05, A Hamiltonian
Fö. 5  03-12-12, A Hamiltonian, Continuation

Christmas Break
Fö. 6  04-01-30, Green's Functions at Zero Temperature
Fö. 7 04-02-06, Wick's Theorem
Fö. 8 04-02-13, Feynman Diagrams
Fö. 9 04-02-20, Feynman Diagrams, Continuation
Fö. 10 04-02-27, Green's Functions at Finite Temperature
Fö. 11  04-03-05, Dyson's Equations
Fö. 12 04-03-12, Rules for Constructing Feynman Diagrams, The Thermodynamic Potential
Fö. 13 04-03-19, Oral Presentations

PART II
Fö. 14  04-03-26, The Electron Gas
Fö. 15 04-04-02, Model Dielectric Functions
Fö. 16  04-04-16, The Energy
Fö. 17  04-04-23, Shortcut Based on Normal Modes
Fö. 18  04-05-07, Vacuum Fluctuations
Fö. 19 04-05-14, The Selfenergy
Fö. 20 04-05-28, Physical Quantities Based on the Energy or Selfenergy
Fö. 21  04-06-04, Physical Quantities Based on the Energy or Selfenergy, Continuation
Fö. 22 04-06-11, The Current-Current Correlation Function
Fö. 23 04-06-18, The Current-Current Correlation Function, Continuation, END









Last update: 2003-11-18, by Bo E. Sernelius