The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory
type: Item
instance of: scholarly article
title: The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory
zbMATH Open document ID: 0573.60076
DOI: 10.1007/BF01206180
author: Michael Aizenman
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: A new approach is presented for the study of the probability that the random paths generated by two independent Brownian motions in \({\mathbb{R}}^ d\) intersect or, more generally, are within a short distance a of each other. The well known behavior of that function of a-above, below, and at the critical dimension \(d=4\), as well as further corrections, are derived here by means of a single renormalization group equation. The equation's derivation is expected to shed some light on the \(\beta\)-function of the \(\lambda \phi^ 4_ d\) quantum field theory.
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 81T17
zbMATH DE Number: 3915363
zbMATH Keywords: intersection of Brownian paths
zbMATH Keywords: renormalization group equation
zbMATH Keywords: quantum field theory
MaRDI profile type: Publication
cites work: On Brownian motions in $n$-space
cites work: Q5794056
cites work: Some intersection properties of random walk paths
cites work: The probability of intersection of independent random walks in four dimensions
cites work: Small distance behaviour in field theory and power counting
cites work: Quantum field theory techniques in graphical enumeration
cites work: Geometric analysis of \(\phi^ 4\) fields and Ising models. I, II
cites work: Intersection properties of simple random walks: A renormalization group approach
full work available at URL: https://doi.org/10.1007/bf01206180
OpenAlex ID: W2048960392
Recommended article: The renormalization group and fractional Brownian motion
Recommended article: Intersection properties of simple random walks: A renormalization group approach
Recommended article: Interacting Brownian particles and Gibbs fields on pathspaces
Recommended article: A rough path perspective on renormalization
Recommended article: On the Renormalization Group Method for the Problem of Random Walk without Self-Intersections
Recommended article: On the path integral formulation of Brownian dynamics
Recommended article: Path integral approach to quantum Brownian motion
Recommended article: On path integrals for the high-dimensional Brownian bridge
Recommended article: Intersections of random walks. A direct renormalization approach
Recommended article: Fermionic path integration and Grassmann Brownian motion
description: scientific article; zbMATH DE number 3915363