Syllabus
The partition function of a quantum system expressed in terms of the functional integral, Bosons and fermions. The relations to the "standard" field theory (at zero temperature), real and imaginary time.
The perturbation expansion of the partition function, the diagrammatic representation. Renormalization, the renormalization group.
Some applications, e.g. the photon gas (QED), spontaneous breakdown and restoration of symmetries in gauge theories, the Higgs model.
Further applications according to interests of students.
References Kapusta: Finite Temperature Field Theory. Cambridge Univ. Press 1989
Parisi: Statistical Field Theory. Addison-Wesley 1988
Negele, H. Orland: Quantum Many-Particle Systems. Addison-Wesley 1988
Fetter, J. D. Walecka: Quantum Theory of Many-Particle Systems. McGraw-Hill 1971
Annotation
The parallels between the statistical physics and the quantum field theory. The technique of the functional integral.
The perturbative expansion of partition function, diagrammatics. Applications to specific problems according to interests of students: e.g.
QCD, kvark-gluon plasma.