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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
Issue Date: 2003
Appears in Collections:Artigo Publicado em Periódico (FIS)

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