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This monograph is the first to present the recently discovered
renormalization techniques for the Schr dinger and Dirac equations,
providing a mathematically rigorous, yet simple and clear
introduction to the subject. It develops field-theoretic techniques
such as Feynman graph expansions and renormalization, taking pains
to make all proofs as simple as possible by using generating
function techniques throughout. Renormalization is performed by
using an exact renormalization group differential equation, a
technique that provides simple but complete proofs of the theorems.
This monograph is the first to present the recently discovered
renormalization techniques for the Schr dinger and Dirac equations,
providing a mathematically rigorous, yet simple and clear
introduction to the subject. It develops field-theoretic techniques
such as Feynman graph expansions and renormalization, taking pains
to make all proofs as simple as possible by using generating
function techniques throughout. Renormalization is performed by
using an exact renormalization group differential equation, a
technique that provides simple but complete proofs of the theorems.
This book collects lecture courses and seminars given at the Les
Houches Summer School 2010 on "Quantum Theory: From Small to Large
Scales." Fundamental quantum phenomena appear on all scales, from
microscopic to macroscopic. Some of the pertinent questions include
the onset of decoherence, the dynamics of collective modes, the
influence of external randomness and the emergence of dissipative
behaviour. Our understanding of such phenomena has been advanced by
the study of model systems and by the derivation and analysis of
effective dynamics for large systems and over long times. In this
field, research in mathematical physics has regularly contributed
results that were recognized as essential in the physics community.
During the last few years, the key questions have been sharpened
and progress on answering them has been particularly strong. This
book reviews the state-of-the-art developments in this field and
provides the necessary background for future studies. All chapters
are written from a pedagogical perspective, making the book
accessible to master and PhD students and researchers willing to
enter this field.
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