From Perturbative to Constructive Renormalization

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Almost surely
Amplitude
Asymptotic analysis
Asymptotic freedom
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Axiom
Borel summation
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Cluster expansion
Coefficient
Combinatorics
Computation
Configuration space
Connectedness
Constructive analysis
Continuous function
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Counting
Coupling constant
Critical exponent
Cumulant
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Derivative
Determinant
Diagram (category theory)
Dimensional regularization
Dirac delta function
Direct proof
Dot product
Effective theory
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Equation
Estimation
Factorial
Feynman–Kac formula
Formal power series
Functional integration
Gauge theory
Gaussian measure
Infimum and supremum
Integration by parts
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Maxima and minima
Maximal set
Minimal subtraction scheme
Momentum
Monomial
N-vector
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Parameter
Path integral formulation
Pauli–Villars regularization
Perturbation theory
Perturbation theory (quantum mechanics)
Phase space
Pointwise
Polynomial
Power series
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Propagator
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Renormalization
Renormalization group
Replica trick
Scale invariance
Schwinger function
softlaunch
Special case
State function
Subsequence
Subset
Subtraction
Summation
Superstring theory
Theorem
Theory
Translational symmetry
Uniform convergence
Wick's theorem
Wightman axioms

Product details

  • ISBN 9780691636825
  • Weight: 652g
  • Dimensions: 152 x 229mm
  • Publication Date: 19 Apr 2016
  • Publisher: Princeton University Press
  • Publication City/Country: US
  • Product Form: Hardback
  • Language: English
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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.