Theoretical Physics: Application of Field Theory to Statistical Mechanics.

E. Brézin

Vladimir V. Bazhanov, Conrad J. Burden

Huzihiro Araki

The significance of operator algebra methods in quantum physics is reviewed for theoretical physicists by examples in application to quantum field theory and quantum statistical mechanics.

Pinaki Majumdar

This chapter discusses phase transitions and symmetry breaking and the mean field approach to condensation in Bose systems and looks at strong interactions in ‘normal’ Fermi systems. ‘Statistical field theory’ encompasses all the applications of quantum field theory to statistical physics. In the context of these notes, it is interpreted as the study of ‘statistical mechanics of quantum many particle systems, employing the methods of field theory’. The identification of the symmetry broken in a phase with long range order allows to construct simple ‘mean field’ theories which provide a qualitative description of the system. Field theoretic methods were those developed by Feynman, Dyson, Schwinger, and others for understanding QED. They were ‘field theoretic’ in that one had to go beyond quantum mechanics, and the Schrodinger equation, to set up a theory. Unlike quantum field theory, there is a Schrodinger equation governing many particle phenomena in condensed matter.

James G. Glimm, Arthur M. Jaffe

James G. Glimm, Arthur M. Jaffe