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 TMF, 2005, Volume 143, Number 3, Pages 375–400 (Mi tmf1820)

Radiation Back-Reaction and Renormalization in Classical Field Theory with Singular Sources

P. O. Kazinski, A. A. Sharapov

Tomsk State University

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 $k\leq2$, the theory becomes not only renormalizable but also finite.

Keywords: radiation back-reaction, strings in background fields, branes in background fields

DOI: https://doi.org/10.4213/tmf1820

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English version:
Theoretical and Mathematical Physics, 2005, 143:3, 798–820

Bibliographic databases:

Citation: P. O. Kazinski, A. A. Sharapov, “Radiation Back-Reaction and Renormalization in Classical Field Theory with Singular Sources”, TMF, 143:3 (2005), 375–400; Theoret. and Math. Phys., 143:3 (2005), 798–820

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf1820
• https://doi.org/10.4213/tmf1820
• http://mi.mathnet.ru/eng/tmf/v143/i3/p375

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Kazinski P.O., “Effective dynamics of an electrically charged string with a current”, Journal of Experimental and Theoretical Physics, 101:2 (2005), 270–279
2. Lechner K., “Radiation reaction and 4-momentum conservation for point-like dyons”, J. Phys. A, 39:37 (2006), 11647–11655
3. Kazinski P.O., “Radiation reaction of multipole moments”, Journal of Experimental and Theoretical Physics, 105:2 (2007), 327–342
4. Lechner K., Marchetti P.A., “Variational principle and energy-momentum tensor for relativistic electrodynamics of point charges”, Annals of Physics, 322:5 (2007), 1162–1190
5. G. F. Efremov, V. V. Sharkov, “Quantum statistical theory of radiation friction of a relativistic electron”, Theoret. and Math. Phys., 158:3 (2009), 406–421
6. Lechner K., “Ultraviolet singularities in classical brane theory”, J. High Energy Phys., 2010, no. 12, 063, 41 pp.
7. Kazinski P.O., Shipulya M.A., “Asymptotics of physical solutions to the Lorentz-Dirac equation for planar motion in constant electromagnetic fields”, Phys Rev E, 83:6, Part 2 (2011), 066606
8. JETP Letters, 101:3 (2015), 206–214
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