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 ℝd 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 β-function of the λø d 4 quantum field theory.
KeywordsBrownian Motion Renormalization Group Intersection Property Critical Dimension Renormalization Group Equation
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