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Type: Artigo de periódico
Title: Clifford valued differential forms, and some issues in gravitation, electromagnetism and "unified" theories
Author: Rodrigues, WA
De Oliveira, EC
Abstract: In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the Lie algebra of Clifford bivectors is isomorphic to the Lie algebra of S1(2, C). In that way the pullback of the linear connection under a local trivialization of the bundle (i.e., a choice of gauge) is represented by a Clifford valued 1-form. That observation makes it possible to realize immediately that Einstein's gravitational theory can be formulated in a way which is similar to a S1(2, C) gauge theory. Such a theory is compared with other interesting mathematical formulations of Einstein's theory, and particularly with a supposedly "unified" field theory of gravitation and electromagnetism proposed by M. Sachs. We show that his identification of Maxwell equations within his formalism is not a valid one. Also, taking profit of the mathematical methods introduced in the paper we investigate a very polemical issue in Einstein gravitational theory, namely the problem of the 'energy-momentum' conservation. We show that many statements appearing in the literature are confusing or even wrong.
Subject: Clifford valued differential forms
Einstein's gravitation
Maxwell equation
Country: Singapura
Editor: World Scientific Publ Co Pte Ltd
Rights: fechado
Identifier DOI: 10.1142/S021827180400581X
Date Issue: 2004
Appears in Collections:Unicamp - Artigos e Outros Documentos

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