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metadata.dc.type: | Artigo de Periódico |
Title: | Nonrelativistic Wave Equations with Gauge Fields |
Other Titles: | International Journal of Theoretical Physics |
Authors: | Santana, Ademir Eugênio de Khanna, Faqir C. Montigny, M. de |
metadata.dc.creator: | Santana, Ademir Eugênio de Khanna, Faqir C. Montigny, M. de |
Abstract: | We illustrate a metric formulation of Galilean invariance by constructing wave equations with gauge fields. It consists of expressing nonrelativistic equations in a covariant form, but with a five-dimensional Riemannian manifold. First we use the tensorial expressions of electromagnetism to obtain the two Galilean limits of electromagnetism found previously by Le Bellac and Lévy-Leblond. Then we examine the nonrelativistic version of the linear Dirac wave equation. With an Abelian gauge field we find, in a weak field approximation, the Pauli equation as well as the spin—orbit interaction and a part reminiscent of the Darwin term. We also propose a generalized model involving the interaction of the Dirac field with a non-Abelian gauge field; the SU(2) Hamiltonian is given as an example. |
Keywords: | Galilean invariance Riemannian geometry Gauge theory Wave equations |
metadata.dc.rights: | Acesso Aberto |
URI: | http://repositorio.ufba.br/ri/handle/ri/14612 |
Issue Date: | 2003 |
Appears in Collections: | Artigo Publicado em Periódico (FIS) |
Files in This Item:
File | Description | Size | Format | |
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A. E. Santana.pdf | 101,68 kB | Adobe PDF | View/Open |
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