dorsal/arxiv
View SchemaPole_Factorization Theorem in Quantum Electrodynamics
| Authors | Henry P. Stapp |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9601008 |
| URL | https://arxiv.org/abs/quant-ph/9601008 |
| Journal | Ann.Poincare 64:479-494,1996 |
Abstract
In quantum electrodynamics a classical part of the S-matrix is normally factored out in order to obtain a quantum remainder that can be treated perturbatively without the occurrence of infrared divergences. However, this separation, as usually performed, introduces spurious large-distance effects that produce an apparent breakdown of the important correspondence between stable particles and poles of the S-matrix, and, consequently, lead to apparent violations of the correspondence principle and to incorrect results for computations in the mesoscopic domain lying between the atomic and classical regimes. An improved computational technique is described that allows valid results to be obtained in this domain, and that leads, for the quantum remainder, in the cases studied, to a physical-region singularity structure that, as regards the most singular parts, is the same as the normal physical-region analytic structure in theories in which all particles have non-zero mass. The key innovations are to define the classical part in coordinate space, rather than in momentum space, and to define there a separation of the photon-electron coupling into its classical and quantum parts that has the following properties: 1) The contributions from the terms containing only classical couplings can be summed to all orders to give a unitary operator that generates the coherent state that corresponds to the appropriate classical process, and 2) The quantum remainder can be rigorously shown to exhibit, as regards its most singular parts, the normal analytic structure.
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"abstract": "In quantum electrodynamics a classical part of the S-matrix is normally\nfactored out in order to obtain a quantum remainder that can be treated\nperturbatively without the occurrence of infrared divergences. However, this\nseparation, as usually performed, introduces spurious large-distance effects\nthat produce an apparent breakdown of the important correspondence between\nstable particles and poles of the S-matrix, and, consequently, lead to apparent\nviolations of the correspondence principle and to incorrect results for\ncomputations in the mesoscopic domain lying between the atomic and classical\nregimes. An improved computational technique is described that allows valid\nresults to be obtained in this domain, and that leads, for the quantum\nremainder, in the cases studied, to a physical-region singularity structure\nthat, as regards the most singular parts, is the same as the normal\nphysical-region analytic structure in theories in which all particles have\nnon-zero mass. The key innovations are to define the classical part in\ncoordinate space, rather than in momentum space, and to define there a\nseparation of the photon-electron coupling into its classical and quantum parts\nthat has the following properties: 1) The contributions from the terms\ncontaining only classical couplings can be summed to all orders to give a\nunitary operator that generates the coherent state that corresponds to the\nappropriate classical process, and 2) The quantum remainder can be rigorously\nshown to exhibit, as regards its most singular parts, the normal analytic\nstructure.",
"arxiv_id": "quant-ph/9601008",
"authors": [
"Henry P. Stapp"
],
"categories": [
"quant-ph"
],
"journal_ref": "Ann.Poincare 64:479-494,1996",
"title": "Pole_Factorization Theorem in Quantum Electrodynamics",
"url": "https://arxiv.org/abs/quant-ph/9601008"
},
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