Radiation back-reaction and renormalization in classical field theory with singular sources

P. O. Kazinski, A. A. Sharapov

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We propose a general covariant method for regularizing the radiation back-reaction in linear and nonlinear field theory models with singular sources. Typical examples of such sources are the currents produced by extended relativistic objects (branes). As an illustration, we consider the models of minimal and nonminimal coupling of a brane to an n-form gauge field, a scalar field, and the Einstein gravity field. We find the structure of divergent and finite contributions due to the radiation back-reaction and obtain relations for the parameters of the theory ensuring cancellation of divergences. We prove that the divergences are Lagrangian n the case where the metric induced on the brane surface is nondegenerate. We find special types of a (nonminimal) coupling leading to local and Lagrangian effective equations of motion of the brane. We show that the requirement for classical renormalizability imposes strong restrictions on the self-coupling vertices of the field, similar to the quantum renormalizability conditions. In particular, we establish the nonrenormalizability of the gravitational self-coupling of a codimension-(k>2) brane, whereas for k ≤ 2, the theory becomes not only renormalizable but also finite.

Original languageEnglish
Pages (from-to)798-820
Number of pages23
JournalTheoretical and Mathematical Physics
Volume143
Issue number3
DOIs
Publication statusPublished - Jun 2005
Externally publishedYes

Fingerprint

Classical Field Theory
Branes
Renormalization
Radiation
radiation
divergence
Divergence
cancellation
Gauge Field
constrictions
equations of motion
apexes
Cancellation
Codimension
Field Theory
Scalar Field
Albert Einstein
gravitation
scalars
Equations of Motion

Keywords

  • Branes in background fields
  • Radiation back-reaction
  • Strings in background fields

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Radiation back-reaction and renormalization in classical field theory with singular sources. / Kazinski, P. O.; Sharapov, A. A.

In: Theoretical and Mathematical Physics, Vol. 143, No. 3, 06.2005, p. 798-820.

Research output: Contribution to journalArticle

@article{db9ed20ae0e2428eaa2991abf89f3d15,
title = "Radiation back-reaction and renormalization in classical field theory with singular sources",
abstract = "We propose a general covariant method for regularizing the radiation back-reaction in linear and nonlinear field theory models with singular sources. Typical examples of such sources are the currents produced by extended relativistic objects (branes). As an illustration, we consider the models of minimal and nonminimal coupling of a brane to an n-form gauge field, a scalar field, and the Einstein gravity field. We find the structure of divergent and finite contributions due to the radiation back-reaction and obtain relations for the parameters of the theory ensuring cancellation of divergences. We prove that the divergences are Lagrangian n the case where the metric induced on the brane surface is nondegenerate. We find special types of a (nonminimal) coupling leading to local and Lagrangian effective equations of motion of the brane. We show that the requirement for classical renormalizability imposes strong restrictions on the self-coupling vertices of the field, similar to the quantum renormalizability conditions. In particular, we establish the nonrenormalizability of the gravitational self-coupling of a codimension-(k>2) brane, whereas for k ≤ 2, the theory becomes not only renormalizable but also finite.",
keywords = "Branes in background fields, Radiation back-reaction, Strings in background fields",
author = "Kazinski, {P. O.} and Sharapov, {A. A.}",
year = "2005",
month = "6",
doi = "10.1007/s11232-005-0107-9",
language = "English",
volume = "143",
pages = "798--820",
journal = "Theoretical and Mathematical Physics(Russian Federation)",
issn = "0040-5779",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Radiation back-reaction and renormalization in classical field theory with singular sources

AU - Kazinski, P. O.

AU - Sharapov, A. A.

PY - 2005/6

Y1 - 2005/6

N2 - We propose a general covariant method for regularizing the radiation back-reaction in linear and nonlinear field theory models with singular sources. Typical examples of such sources are the currents produced by extended relativistic objects (branes). As an illustration, we consider the models of minimal and nonminimal coupling of a brane to an n-form gauge field, a scalar field, and the Einstein gravity field. We find the structure of divergent and finite contributions due to the radiation back-reaction and obtain relations for the parameters of the theory ensuring cancellation of divergences. We prove that the divergences are Lagrangian n the case where the metric induced on the brane surface is nondegenerate. We find special types of a (nonminimal) coupling leading to local and Lagrangian effective equations of motion of the brane. We show that the requirement for classical renormalizability imposes strong restrictions on the self-coupling vertices of the field, similar to the quantum renormalizability conditions. In particular, we establish the nonrenormalizability of the gravitational self-coupling of a codimension-(k>2) brane, whereas for k ≤ 2, the theory becomes not only renormalizable but also finite.

AB - We propose a general covariant method for regularizing the radiation back-reaction in linear and nonlinear field theory models with singular sources. Typical examples of such sources are the currents produced by extended relativistic objects (branes). As an illustration, we consider the models of minimal and nonminimal coupling of a brane to an n-form gauge field, a scalar field, and the Einstein gravity field. We find the structure of divergent and finite contributions due to the radiation back-reaction and obtain relations for the parameters of the theory ensuring cancellation of divergences. We prove that the divergences are Lagrangian n the case where the metric induced on the brane surface is nondegenerate. We find special types of a (nonminimal) coupling leading to local and Lagrangian effective equations of motion of the brane. We show that the requirement for classical renormalizability imposes strong restrictions on the self-coupling vertices of the field, similar to the quantum renormalizability conditions. In particular, we establish the nonrenormalizability of the gravitational self-coupling of a codimension-(k>2) brane, whereas for k ≤ 2, the theory becomes not only renormalizable but also finite.

KW - Branes in background fields

KW - Radiation back-reaction

KW - Strings in background fields

UR - http://www.scopus.com/inward/record.url?scp=21644446309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21644446309&partnerID=8YFLogxK

U2 - 10.1007/s11232-005-0107-9

DO - 10.1007/s11232-005-0107-9

M3 - Article

VL - 143

SP - 798

EP - 820

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 3

ER -