The Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory
Copyright policy )The Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory
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.
- Rutgers, The State University of New Jersey United States
Renormalization group methods applied to problems in quantum field theory, 60J65, Stochastic mechanics (including stochastic electrodynamics), 82A25, renormalization group equation, 81E15, quantum field theory, Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.), intersection of Brownian paths
Renormalization group methods applied to problems in quantum field theory, 60J65, Stochastic mechanics (including stochastic electrodynamics), 82A25, renormalization group equation, 81E15, quantum field theory, Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.), intersection of Brownian paths
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).40 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!