Many-Body Physics

Recommended Prerequisites

Basic knowledge of Quantum Mechanics.

Teaching Methods

This course will combine theoretical and exercise problem sheets in such a way that the student can acquire the techniques to investigate Many-Body Systems. The concepts will then be worked out by the study of applications always present during the course.

Learning Outcomes

The main goal of this course is to provide the theoretical framework for the understanding of the behaviour of quantum mechanical systems with a large number of interacting particles. The large number of particles can be between three and infinity with examples spreading from Nuclear and Particle Physics to Condensed Matter Physics and Atomic and Molecular Physics.

Work Placement(s)

No

Syllabus

1.Second quantisation and applications
1.1 Mean field theory
1.2 The Hartree-Fock theory

2.Functional Integrals
2.1 Grassmann variables
2.2 Coherent states
2.3 Functional representation of the partition function

3. Linear Response Theory
3.1 Analytical properties of the Green functions
3.2 The fluctuation-dissipation theorem

4. Perturbative Expansion and diagrammatic representation
4.1 Spectral representations for the Green functions
4.2 The Matsubara formalism
4.3 Wick theorem and Feynman diagrams

5. Applications.

Head Lecturer(s)

Fernando Manuel Silva Nogueira

Assessment Methods

Assessment
Review and presentation of a scientific article : 10.0%
Frequency: 40.0%
Project: 50.0%

Bibliography

1.Segunda quantização e aplicações
P. Coleman: "Introduction to Many-Body Physics"
G. D. Mahan: "Many-particle physics”
A. Altland, B. Simons: "Condensed Matter Field Theory"
J. W. Negele, H. Orland: "Quantum Many-Particle Systems"
H. Bruus, K. Flensberg: "Many-Body Quantum Theory in Condensed Matter Physics: An Introduction"
J.-P.Blaizot, G. Ripka, “Quantum Theory of Finite Systems”
E. K. U. Gross, E. Runge, O. Heinonen, “Many-Particle Theory”
A. L. Fetter, J. D. Walecka, “Quantum Theory of Many-Particle Systems”
J. I. Kapusta, C. Gale, “Finite-Temperature Field Theory Principles and Applications”.