zbMATH — the first resource for mathematics

On quantum fields and systems with ordered ground state. (English) Zbl 0872.58079
The monograph discusses certain aspects of and reviews work on physical systems with ordered ground states using the formalism of quantum field theory. The first part deals with the quantum Hall effect and the anyon description of superconductivity, while the second part addresses specific properties like convexity of the effective potential and the high temperature behavior of models with a Higgs doublet. The quantum Hall effect is approached via topological field theory (Chern-Simons theory), and a 2+1 dimensional relativistic field is used to study the Meissner effect in planar superconducting matter. Then Bogoliubov’s method of quasi-averages and path integral representations of certain functionals (generating Green functions) are employed to define the effective potential. When applied to the Higgs model these methods suggest that the (gauge) symmetry may be spontaneously broken in some temperature interval, while being unbroken at zero and high temperature.
58Z05 Applications of global analysis to the sciences
82B99 Equilibrium statistical mechanics
81T99 Quantum field theory; related classical field theories
82D55 Statistical mechanics of superconductors
82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics
PDF BibTeX Cite
Full Text: EMIS EuDML