Stochastic theory of relativistic particles moving in a quantum field: Scalar Abraham-Lorentz-Dirac-Langevin equation, radiation reaction, and vacuum fluctuations

2001/01/31 by Philip R. Johnson, B. L. Hu · 142 citations
Computer Science · Physics and Astronomy · #Classical mechanics #Langevin equation #Physics #Quantization (signal processing) #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum decoherence #Quantum electrodynamics #Quantum field theory #Quantum mechanics #Scalar field #Semiclassical physics #gr-qc #hep-ph #quant-ph

paper · pdf · doi:10.1103/physrevd.65.065015

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 65(6) (American Physical Society) · RevTex; 20 pages, 3 figures, Replaced version has corrected typos, slightly modified derivation, improved discussion including new section with comparisons to related work, and expanded references

arxiv created 2001/06/01 · openalex publication_date 2002/02/28 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We apply the open systems concept and the influence functional formalism to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the quantum and semiclassical regimes captures the statistical mechanical attributes of the full theory. Applying the particle-centric world line quantization formulation to describe charged particles in a scalar quantum field environment, we derive a modified Abraham-Lorentz-Dirac (ALD) equation with time-dependent coefficients and show that it is the correct semiclassical limit for nonlinear particle-field systems without the need of making the dipole or nonrelativistic approximations. Our modified ALD equation is causal and free of runaway solutions. We show this technically, as a consequence of the nonequilibrium open system dynamics, and conceptually, invoking decoherence. Progressing to the stochastic regime, we derive a relativistic ALD-Langevin (ALDL) equation for nonlinearly coupled charges in a scalar quantum field. The ALD and ALDL equations clarify the relation of radiation reaction, dissipation and vacuum fluctuations. This self-consistent treatment serves as a new platform for investigations into problems related to relativistic moving charges.

Citations

• Self-Energy and Stability of the Classical Electron
• Worldline Green functions for multiloop diagrams
• Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction
• Run-away Electrons in Relativistic Spin 12 Quantum Electrodynamics
• Quantum tunnelling in a dissipative system
• Consistent Sets Yield Contrary Inferences in Quantum Theory
• Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?
• On the generalized ward identity
• Interaction with the Absorber as the Mechanism of Radiation
• Irreversibility and Generalized Noise
• Radiation reaction and the nonrelativistic theory of the electron
• Classical and quantum mechanics of the damped harmonic oscillator
• Hard thermal loops and beyond in the finite temperature world-line formulation of QED
• Environment-induced superselection rules
• On Gauge Invariance and Vacuum Polarization
• An Identity in Quantum Electrodynamics
• Stochastic behavior of effective field theories across the threshold
• Transport, Collective Motion, and Brownian Motion
• Dynamics of the dissipative two-state system
• Decoherence of hydrodynamic histories: A simple spin model
• Phase-space decoherence: A comparison between consistent histories and environment-induced superselection
• Stochastic Gravity

Cited by

• Emergent/quantum gravity: macro/micro structures of spacetime
• Signatures of the quantization of gravity at gravitational wave detectors
• Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect
• Stochastic gravity: a primer with applications
• Brownian Emitters
• Intrinsic and fundamental decoherence: issues and problems
• Unruh effect under non-equilibrium conditions: oscillatory motion of an Unruh-DeWitt detector
• Relativistic quantum information in detectors–field interactions
• Self-force on extreme mass ratio inspirals via curved spacetime effective field theory