The intersection of Brownian paths as a case study of a renormalization group method for quantum field theory

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Abstract

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 λφd4 quantum field theory.

Original languageEnglish (US)
Pages (from-to)91-110
Number of pages20
JournalCommunications In Mathematical Physics
Volume97
Issue number1-2
DOIs
StatePublished - Mar 1 1985
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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