In interaction the between the leads to a quantum liquids particles
variety of and unusual states of condensed matter interesting
systems, super e.g. and the fractional in electron Hall effect
conductivity quantum (FQHE) sys tems. In this book for we
investigate quantum field theoretical approaches fermion the is
interacting systems. Originally, quantum fieldtheory designed
describe as a to perturbation theory weakly interacting many
particle sys tems. For treatment of interaction and correlation
effects a proper beyond the the series of must beresummed
perturbation theory, Feynmandiagrams severalresummationschemeswhich
the We on partially. present depend par ticular effect
considered.We start with ofthe a physical compactdescription self
consistent and the quantum fieldtheory approximations. conserving
the of in fermion is caused two Superconductivity systems by
interplay formation ofbound attractive interaction between the
phenomena: pairsby fermions condensation ofthe low to and at
temperatures leading long pairs order and We consider three
dimensional of a range superfluidity. system fermionswith
attractiveinteractionwhichshowsacrossoverfrom short range BCS to
Bose Einstein condensation ofbound ifthe superconductivity pairs
interaction is tuned fromweak to While the self coupling. strength
strong consistent version ofthe is well suited to describe con
quantum field theory densation of and a second resummation to the
pairs superfluidity, leading the ofbound Bethe Salpeter equation
describes formation pairs.
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