Methods and Models for Strongly Correlated Systems

  Teacher: Professor You-Quan Li

     The main purpose of this course is to provide for advanced graduated students whose major are theoretical condensed matter physics, or for those who  like to pursue research in the application of quantum field theory method  to the current topics in theoretical physics.




Reference text books

L.D. Landau and E.M. Lifshitz 《Quantum Mechanics-nonrelativistic theory》 

M. Stone,《The Physics of Quantum Field Theory》
N. Nagaosa,《Quantum Field Theory in Condensed Matter Physics》
K. Huang 《Quantum Field Theory--from operators to path integrals》

N. Nagaosa Quantum Field Theory in Strongly Correlated Electronic Systems

A.Gogolin,A.Nersesyan and A.TsvelikBosonization and Strongly Correlated Systems
E.FradkinField theory of condensed matter physics
Field theories for low-dimensional condensed matter systems

Online references:

H.Kleinert, Gauge theory in condensed matter physics

Tentative contents

Mathematics thoughts refreshment: from primary school to college levels


Quantum mechanics background:  brief survey and  further supplements

1.Survey of approximation methods
   Perturbation,Ritz,WKB,Bonn-Obenheimer,Thomas-Fermi,Hartee-Fock & Adiabatic approximations   

2.Representations,pictures and canonical transformation

Schrodinger,Heisenberg,Interaction | Backer-Hausdorf formula

In and Out | Lippmann-Schwinger equation

Reprsentations: coordinate,momentum,energy,Fock,& action-angle

Fourier transform and uncertainty | coherent state & squeezed state

Model versus spectrum, an example model of canonical transformation

3.Symmetry versus conservation, gauge and boundary condition 
 [Landau's book, Byer-Yang paper]

Many-body system  via field theory  

0.Classification of solids | The many-body problem
1.Derivation to scalar field equation
The S-matrix expansion and Feynman diagrams 

Path integral and its application 

[background resources: 费曼路经积分 导引 more and more]

Symmetry breaking and phase transition

[background resources: K-T 相变  more ]

Coulomb gas and supperfluidity

[background resources: supperfluidity(理论, 实验)    玻色爱因斯坦凝聚 ]

Superconductivity related problems  

[background resources: 超导简介  Vortex ]

Quantum Hall liquid  

[background resources: 量子霍耳效应   more and more ]

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