From Perturbative to Constructive Renormalization (eBook)

V. Rivasseau (Autor)

eBook Download: PDF

2014
348 Seiten
Princeton University Press (Verlag)
978-1-4008-6208-5 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 14.7.2014
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Series in Physics
• Reihe/Serie: Princeton Series in Physics
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• Schlagworte: absolute convergence • absolute value • Almost surely • Amplitude • analytic continuation • Ansatz • asymptotic analysis • asymptotic freedom • Axiom • Big O notation • bilinear form • Borel summation • Boundary value problem • Canonical commutation relation • Change of variables • Cluster expansion • coefficient • combinatorics • Computation • Configuration space • connectedness • Constructive analysis • continuous function • Continuous function (set theory) • Counting • coupling constant • covariant derivative • critical exponent • Cumulant • Derivative • Determinant • Diagonalizable matrix • Diagram (category theory) • Dimensional regularization • Dirac delta function • Direct proof • dot product • Effective action • effective potential • Effective theory • Equation • equivalence class • equivalence relation • estimation • exterior derivative • factorial • Feynman–Kac formula • Formal power series • fourier analysis • functional integration • Gauge Theory • Gaussian measure • Incidence matrix • Infimum and supremum • Integration by parts • Lebesgue measure • Linearity • Maxima and minima • Maximal set • Mean field theory • Measurable function • Minimal subtraction scheme • Momentum • Monomial • N-vector • ORDER BY • orthogonal polynomials • Parameter • partial derivative • Path integral formulation • Pauli–Villars regularization • Permutation • perturbation theory • Perturbation theory (quantum mechanics) • Phase space • Pointwise • polynomial • power series • principal bundle • Propagator • Reciprocal Lattice • renormalization • Renormalization Group • Replica Trick • scale invariance • Schwinger function • Special case • State function • subsequence • Subset • subtraction • Summation • Superstring Theory • Theorem • theory • Translational symmetry • uniform convergence • Wick's theorem • Wightman axioms • Yang–Mills Theory
• ISBN-10: 1-4008-6208-6 / 1400862086
• ISBN-13: 978-1-4008-6208-5 / 9781400862085