Perturbative quantum analysis and classical limit of the electron scattering by a solenoidal magnetic field Export

@article{citeulike:4148500, 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 non-relativistic 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 non-perturbative methodology should be applied.}, archivePrefix = {arXiv}, author = {Murguia, Gabriela and Moreno, Matias and Torres, Manuel}, citeulike-article-id = {4148500}, citeulike-linkout-0 = {http://arxiv.org/abs/0903.0427}, citeulike-linkout-1 = {http://arxiv.org/pdf/0903.0427}, day = {3}, eprint = {0903.0427}, keywords = {calculation, electrodynamics, perturbation\_theory, quantum\_electrodynamics, scattering\_theory}, month = {Mar}, posted-at = {2009-03-08 10:50:33}, priority = {2}, title = {Perturbative quantum analysis and classical limit of the electron scattering by a solenoidal magnetic field}, url = {http://arxiv.org/abs/0903.0427}, year = {2009} }

TY - JOUR ID - citeulike:4148500 L3 - citeulike-article-id:4148500 N2 - 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 non-relativistic 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 non-perturbative methodology should be applied. TI - Perturbative quantum analysis and classical limit of the electron scattering by a solenoidal magnetic field KW - calculation KW - electrodynamics KW - perturbation_theory KW - quantum_electrodynamics KW - scattering_theory AU - Murguia, Gabriela AU - Moreno, Matias AU - Torres, Manuel PY - 2009/Mar/03/ UR - http://arxiv.org/abs/0903.0427 ER -