Modern techniques from quantum field theory are applied in this
work to the description of ultracold quantum gases. This leads to a
unified description of many phenomena including superfluidity for
bosons and fermions, classical and quantum phase transitions,
different dimensions, thermodynamic properties and few-body
phenomena as bound state formation or the Efimov effect. The
non-perturbative treatment with renormalization group flow
equations can account for all known limiting cases by solving one
single equation. It improves previous results quantitatively and
brings qualitatively new insights. As an example, new quantum phase
transitions are found for fermions with three spin states.
Ultracold atomic gases can be seen as an interesting model for
features of high energy physics and for condensed matter theory.
The research reported in this thesis helps to solve the difficult
complexity problem in modern theoretical physics.
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