**Fields Institute Communications**

Volume: 50;
2007;
404 pp;
Hardcover

MSC: Primary 81; 76; 60; 30; 82;

Print ISBN: 978-0-8218-4273-7

Product Code: FIC/50

List Price: $130.00

Individual Member Price: $104.00

**Electronic ISBN: 978-1-4704-3084-9
Product Code: FIC/50.E**

List Price: $130.00

Individual Member Price: $104.00

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# Universality and Renormalization: From Stochastic Evolution to Renormalization of Quantum Fields

Share this page *Edited by *
*Ilia Binder; Dirk Kreimer*

A co-publication of the AMS and Fields Institute

This book covers a wide range of phenomena in the natural sciences dominated by notions of universality and renormalization. The contributions in this volume are equally broad in their approach to these phenomena, offering the mathematical as well as the perspective of the applied sciences. They explore renormalization theory in quantum field theory and statistical physics, and its connections to modern mathematics as well as physics on scales from the microscopic to the macroscopic.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Table of Contents

# Table of Contents

## Universality and Renormalization: From Stochastic Evolution to Renormalization of Quantum Fields

- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- Manifestly gauge invariant exact renormalization groups 18
- SLE(8/3) and Brownian excursions in annuli 2734
- Cardy’s formula on the triangular lattice, the easy way 3946
- Rota-Baxter algebras in renormalization of perturbative quantum field theory 4754
- Practicalities of renormalizing quantum field theories 107114
- Quantum field theory in curved spacetime 131138
- Entropy of 𝑋𝑌 spin chain and block Toeplitz determinants 151158
- On the quantitative boundary behavior of SLE 185192
- The configurational measure on mutually avoiding SLE paths 199206
- Dyson-Schwinger equations: From Hopf algebra to number theory 225232
- Two-sided 𝑆𝐿𝐸_{8/3} and the infinite self-avoiding polygon 249256
- Using the renormalization group 281288
- Short distance behavior of scaling functions for the planar ising model 307314
- Constructing conformal field theory models 317324
- The art of computing loop integrals 345352
- The transition temperature of the weakly interacting Bose gas 397404
- Back Cover Back Cover1414

#### Readership

Graduate students and research mathematicians interested in quantum field theory, statistical physics, physics and number theory, nonlinear dynamics, probability,geometic function theory, differential equations.