Perturbative Quantum Analysis and Classical Limit of the Electron Scattering by a Solenoidal Magnetic Field
Abstract
A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the nonrelativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable nonperturbative methodology should be applied.
 Authors:
 Departamento de Fisica, Facultad de Ciencias, UNAM. Apartado postal 70542, 04510, Mexico, D.F. (Mexico)
 Instituto de Fisica, UNAM. Apartado postal 20364, 01000, Mexico, D.F. (Mexico)
 Publication Date:
 OSTI Identifier:
 21300488
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: AIP Conference Proceedings; Journal Volume: 1116; Journal Issue: 1; Conference: 13. Mexican school of particles and fields, Hermosillo (Mexico); San Carlos (Mexico), 211 Oct 2008; Other Information: DOI: 10.1063/1.3131576; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AHARONOVBOHM EFFECT; CORRECTIONS; COULOMB SCATTERING; DIFFERENTIAL CROSS SECTIONS; ELECTRONELECTRON INTERACTIONS; ELECTRONS; MAGNETIC FIELDS; PERTURBATION THEORY; QUANTUM ELECTRODYNAMICS; RELATIVISTIC RANGE; SOLENOIDS
Citation Formats
Murguia, Gabriela, Moreno, Matias, and Torres, Manuel. Perturbative Quantum Analysis and Classical Limit of the Electron Scattering by a Solenoidal Magnetic Field. United States: N. p., 2009.
Web. doi:10.1063/1.3131576.
Murguia, Gabriela, Moreno, Matias, & Torres, Manuel. Perturbative Quantum Analysis and Classical Limit of the Electron Scattering by a Solenoidal Magnetic Field. United States. doi:10.1063/1.3131576.
Murguia, Gabriela, Moreno, Matias, and Torres, Manuel. 2009.
"Perturbative Quantum Analysis and Classical Limit of the Electron Scattering by a Solenoidal Magnetic Field". United States.
doi:10.1063/1.3131576.
@article{osti_21300488,
title = {Perturbative Quantum Analysis and Classical Limit of the Electron Scattering by a Solenoidal Magnetic Field},
author = {Murguia, Gabriela and Moreno, Matias and Torres, Manuel},
abstractNote = {A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the nonrelativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable nonperturbative methodology should be applied.},
doi = {10.1063/1.3131576},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1116,
place = {United States},
year = 2009,
month = 4
}

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