Functional Renormalization Group for Interacting Bosons
The physics of interacting bosons in the phase with broken symmetry
is very different from the physics in the symmetric phase. The
Functional Renormalization Group (FRG) represents a powerful
investigation method which allows the description of symmetry
breaking with high efficiency. In this book we apply FRG for
studying two different models in the broken symmetry phase. In the
first part we consider the classical O(1)-model in the vicinity of
the second order phase transition. Employing a truncation scheme
based on relevance of coupling parameters we study the behavior of
the RG-flow which is influenced by the competition between two
characteristic lengths of the system. We calculate momentum
dependent self-energy and study its dependence on both length
scales. In the second part we apply the FRG-formalism to systems of
interacting bosons in arbitrary spatial dimensions at zero
temperature. We use a truncation scheme based on a non-local
potential approximation which satisfy both exact relations
postulated by Hugenholtz and Pines, and Nepomnyashchy and
Nepomnyashchy. We discuss different scaling regimes and calculate
the single-particle spectral density function.
Studied electrical engineering at the Kazan State University of Technology (RUS) and physics at the Technical University of Brunswick (GER). He acquired Dr.-Ing. from the Tupolev Technical State University of Kazan (RUS) and Dr. phil. nat. from the Goethe University of Frankfurt. He is currently working at the University of Augsburg.
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