From Perturbative to Constructive Renormalization

V. Rivasseau (Autor)

Buch | Softcover

348 Seiten

2014
Princeton University Press (Verlag)
978-0-691-60835-8 (ISBN)

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The last decade has seen striking progress in the subject of renormalization in quantum field theory. The old subject of perturbative renormalization has been revived by the use of powerful methods such as multiscale decompositions; precise estimates have been added to the initial theorems on finiteness of renormalized perturbation theory, with new results on its large order asymptotics. Furthermore, constructive field theory has reached one of its major goals, the mathematically rigorous construction of some renormalizable quantum field theories. For these models one can in particular investigate rigorously the phenomenon of asymptotic freedom, which plays a key role in our current understanding of the interaction among elementary particles. However, until this book, there has been no pedagogical synthesis of these new developments. Vincent Rivasseau, who has been actively involved in them, now describes them for a wider audience. There are, in fact, common concepts at the heart of the progress on perturbative and constructive techniques.
Exploiting these similarities, the author uses perturbative renormalization, which is the more widely known and conceptually simpler of the two cases, to explain the less familiar but more mathematically meaningful constructive renormalization. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

*FrontMatter, pg. i*Contents, pg. vii*Acknowledgements, pg. ix*Chapter I.1 The Ultraviolet Problem, pg. 3*Chapter I.2 Euclidean Field Theory. The O.S. Axioms, pg. 15*Chapter I.3 The PHI4 Model, pg. 23*Chapter I.4 Feynman Graphs and Amplitudes, pg. 37*Chapter I.5 Borel Summability, pg. 54*Chapter II.1 The Multiscale Representation and a Bound on Convergent Graphs, pg. 59*Chapter II.2 Renormalization Theory for PHI44, pg. 74*Chapter II.3 Proof of the Uniform BPH Theorem, pg. 90*Chapter II.4 The Effective Expansion, pg. 111*Chapter II.5 Construction of "Wrong Sign" Planar PHI44, pg. 123*Chapter II.6 The Large Order Behavior of Perturbation Theory, pg. 144*Chapter III.1 Single Scale Cluster and Mayer Expansions, pg. 171*Chapter III.2 The Phase Space Expansion: The Convergent Case, pg. 210*Chapter III.3 The Effective Expansion and Infrared PHI44, pg. 241*Chapter III.4 The Gross-Neveu Model, pg. 272*Chapter III.5 The Ultraviolet Problem in Non-Abelian Gauge Theories, pg. 289*References and Bibliography, pg. 321*Index, pg. 333

Erscheint lt. Verlag	14.7.2014
Reihe/Serie	Princeton Legacy Library
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 229 mm
Gewicht	482 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
ISBN-10	0-691-60835-0 / 0691608350
ISBN-13	978-0-691-60835-8 / 9780691608358
Zustand	Neuware