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  Motion in classical field theories and the foundations of the self-force problem

Harte, A. I. (2016). Motion in classical field theories and the foundations of the self-force problem. In Equations of Motion in Relativistic Gravity (Fundamental Theories of Physics, 179) (pp. 327-398). Heidelberg u.a.: Springer.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0019-83F1-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-23D5-2
Genre: Book Chapter

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1405.5077.pdf (Preprint), 881KB
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 Creators:
Harte, Abraham I.1, Author              
Affiliations:
1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24013              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP, Physics, Classical Physics, physics.class-ph
 Abstract: This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and self-torque are derived using simple, non-perturbative arguments. The relevant concepts are developed gradually by considering motion in a series of increasingly complicated theories. Newtonian gravity is discussed first, then Klein-Gordon theory, electromagnetism, and finally general relativity. Linear and angular momenta as well as centers of mass are defined in each of these cases. Multipole expansions for the force and torque are then derived to all orders for arbitrarily self-interacting extended objects. These expansions are found to be structurally identical to the laws of motion satisfied by extended test bodies, except that all relevant fields are replaced by effective versions which exclude the self-fields in a particular sense. Regularization methods traditionally associated with self-interacting point particles arise as straightforward perturbative limits of these (more fundamental) results. Additionally, generic mechanisms are discussed which dynamically shift --- i.e., renormalize --- the apparent multipole moments associated with self-interacting extended bodies. Although this is primarily a synthesis of earlier work, several new results and interpretations are included as well.

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 Dates: 2014-05-202016
 Publication Status: Published in print
 Pages: 68 pages, 1 figure, review for WE-Heraeus seminar on "Equations of motion in relativistic gravity"
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 Identifiers: arXiv: 1405.5077
DOI: 10.1007/978-3-319-18335-0_12
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Title: Equations of Motion in Relativistic Gravity (Fundamental Theories of Physics, 179)
Source Genre: Book
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Publ. Info: Heidelberg u.a. : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 327 - 398 Identifier: -