Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space

Chad R. Galley, B. L. Hu, Shih Yuin Lin

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, describing the motion of an electric point charge sourcing an electromagnetic field, which backreacts on the charge as a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equation describing the motion of a point mass with self-force interacting with the linearized metric perturbations caused by the mass off an otherwise vacuous curved background spacetime. We regularize the formally divergent self-force by smearing the direct part of the retarded Green's function and using a quasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevin equations with a classical stochastic force accounting for the effect of the quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. These equations will be useful for studying the stochastic motion of charges and small masses under the influence of both quantum and classical noise sources, derived either self-consistently or put in by hand phenomenologically. We also show that history-dependent noise-induced drift motions could arise from such stochastic sources on the trajectory that could be a hidden feature of gravitational wave forms hitherto unknown.

Original languageEnglish
Article number024017
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume74
Issue number2
DOIs
Publication statusPublished - 2006 Jul 24

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relativistic particles
Quantum Fields
electromagnetism
Motion
Charge
Particle Trajectory
Quantum Fluctuations
particle trajectories
Langevin Equation
Dirac Equation
Gravitational Waves
Dirac equation
Waveform
gravitational waves
Electromagnetic Fields
Paul Adrien Maurice Dirac
Green's function
electromagnetic fields
Green's functions
derivation

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

Cite this

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abstract = "We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, describing the motion of an electric point charge sourcing an electromagnetic field, which backreacts on the charge as a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equation describing the motion of a point mass with self-force interacting with the linearized metric perturbations caused by the mass off an otherwise vacuous curved background spacetime. We regularize the formally divergent self-force by smearing the direct part of the retarded Green's function and using a quasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevin equations with a classical stochastic force accounting for the effect of the quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. These equations will be useful for studying the stochastic motion of charges and small masses under the influence of both quantum and classical noise sources, derived either self-consistently or put in by hand phenomenologically. We also show that history-dependent noise-induced drift motions could arise from such stochastic sources on the trajectory that could be a hidden feature of gravitational wave forms hitherto unknown.",
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N2 - We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, describing the motion of an electric point charge sourcing an electromagnetic field, which backreacts on the charge as a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equation describing the motion of a point mass with self-force interacting with the linearized metric perturbations caused by the mass off an otherwise vacuous curved background spacetime. We regularize the formally divergent self-force by smearing the direct part of the retarded Green's function and using a quasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevin equations with a classical stochastic force accounting for the effect of the quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. These equations will be useful for studying the stochastic motion of charges and small masses under the influence of both quantum and classical noise sources, derived either self-consistently or put in by hand phenomenologically. We also show that history-dependent noise-induced drift motions could arise from such stochastic sources on the trajectory that could be a hidden feature of gravitational wave forms hitherto unknown.

AB - We provide a quantum field theoretical derivation of the Abraham-Lorentz-Dirac (ALD) equation, describing the motion of an electric point charge sourcing an electromagnetic field, which backreacts on the charge as a self-force, and the Mino-Sasaki-Tanaka-Quinn-Wald (MSTQW) equation describing the motion of a point mass with self-force interacting with the linearized metric perturbations caused by the mass off an otherwise vacuous curved background spacetime. We regularize the formally divergent self-force by smearing the direct part of the retarded Green's function and using a quasilocal expansion. We also derive the ALD-Langevin and the MSTQW-Langevin equations with a classical stochastic force accounting for the effect of the quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. These equations will be useful for studying the stochastic motion of charges and small masses under the influence of both quantum and classical noise sources, derived either self-consistently or put in by hand phenomenologically. We also show that history-dependent noise-induced drift motions could arise from such stochastic sources on the trajectory that could be a hidden feature of gravitational wave forms hitherto unknown.

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