dorsal/arxiv
View SchemaStochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations
| Authors | Philip R. Johnson, B. L. Hu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0101001 |
| URL | https://arxiv.org/abs/quant-ph/0101001 |
| DOI | 10.1103/PhysRevD.65.065015 |
| Journal | Phys.Rev.D65:065015,2002 |
Abstract
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the quantum and semi-classical captures the statistical mechanical attributes of the full theory. Applying the particle-centric world-line quantization formulation to the quantum field theory of scalar QED we derive a time-dependent (scalar) Abraham-Lorentz-Dirac (ALD) equation and show that it is the correct semiclassical limit for nonlinear particle-field systems without the need of making the dipole or non-relativistic approximations. Progressing to the stochastic regime, we derive multiparticle ALD-Langevin equations for nonlinearly coupled particle-field systems. With these equations we show how to address time-dependent dissipation/noise/renormalization in the semiclassical and stochastic limits of QED. We clarify the the relation of radiation reaction, quantum dissipation and vacuum fluctuations and the role that initial conditions may play in producing non-Lorentz invariant noise. We emphasize the fundamental role of decoherence in reaching the semiclassical limit, which also suggests the correct way to think about the issues of runaway solutions and preacceleration from the presence of third derivative terms in the ALD equation. We show that the semiclassical self-consistent solutions obtained in this way are ``paradox'' and pathology free both technically and conceptually. This self-consistent treatment serves as a new platform for investigations into problems related to relativistic moving charges.
{
"annotation_id": "665bbdf4-a8e5-46a3-91b8-2b8436c10c66",
"date_created": "2026-03-02T18:01:42.264000Z",
"date_modified": "2026-03-02T18:01:42.264000Z",
"file_hash": "a5839142c3f2c23d7b30b14bfffbdeaca72bfc8b5d8d2a6af5949d11a333eff7",
"private": false,
"record": {
"abstract": "We apply the open systems concept and the influence functional formalism\nintroduced in Paper I to establish a stochastic theory of relativistic moving\nspinless particles in a quantum scalar field. The stochastic regime resting\nbetween the quantum and semi-classical captures the statistical mechanical\nattributes of the full theory. Applying the particle-centric world-line\nquantization formulation to the quantum field theory of scalar QED we derive a\ntime-dependent (scalar) Abraham-Lorentz-Dirac (ALD) equation and show that it\nis the correct semiclassical limit for nonlinear particle-field systems without\nthe need of making the dipole or non-relativistic approximations. Progressing\nto the stochastic regime, we derive multiparticle ALD-Langevin equations for\nnonlinearly coupled particle-field systems. With these equations we show how to\naddress time-dependent dissipation/noise/renormalization in the semiclassical\nand stochastic limits of QED. We clarify the the relation of radiation\nreaction, quantum dissipation and vacuum fluctuations and the role that initial\nconditions may play in producing non-Lorentz invariant noise. We emphasize the\nfundamental role of decoherence in reaching the semiclassical limit, which also\nsuggests the correct way to think about the issues of runaway solutions and\npreacceleration from the presence of third derivative terms in the ALD\nequation. We show that the semiclassical self-consistent solutions obtained in\nthis way are ``paradox\u0027\u0027 and pathology free both technically and conceptually.\nThis self-consistent treatment serves as a new platform for investigations into\nproblems related to relativistic moving charges.",
"arxiv_id": "quant-ph/0101001",
"authors": [
"Philip R. Johnson",
"B. L. Hu"
],
"categories": [
"quant-ph",
"gr-qc",
"hep-ph"
],
"doi": "10.1103/PhysRevD.65.065015",
"journal_ref": "Phys.Rev.D65:065015,2002",
"title": "Stochastic Theory of Relativistic Particles Moving in a Quantum Field: II. Scalar Abraham-Lorentz-Dirac-Langevin Equation, Radiation Reaction and Vacuum Fluctuations",
"url": "https://arxiv.org/abs/quant-ph/0101001"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "3b44cb03-58e4-4943-9077-ceb700ea85c0",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}