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

Michael Aizenman

doi:10.1007/BF01206180

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

Michael Aizenman

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

A new approach is presented for the study of the probability that the random paths generated by two independent Brownian motions in 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 β-function of the λφ_d⁴ quantum field theory.

Original language	English (US)
Pages (from-to)	91-110
Number of pages	20
Journal	Communications In Mathematical Physics
Volume	97
Issue number	1-2
DOIs	https://doi.org/10.1007/BF01206180
State	Published - Mar 1985
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01206180

Cite this

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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.",

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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