Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/323269
Type: Artigo
Title: The Clifford Algebra Of Physical Space And Dirac Theory
The Clifford algebra of physical space and Dirac theory
Author: Vaz Jr. Jayme
Abstract: The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli matrices is shown to not be completely true. It is only true as long as the term βψ in the usual Dirac factorization of the Klein-Gordon equation is assumed to be the product of a square matrix β and a column matrix ψ. In this paper we show that there is another possibility besides this matrix product, in fact a possibility involving a matrix operation, and show that it leads to another possible expression for the Dirac equation. We show that, behind this other possible factorization is the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss several different aspects of Dirac theory using this formalism. In particular, we show that there are four different possible sets of definitions for the parity, time reversal, and charge conjugation operations for the Dirac equation. © 2016 IOP Publishing Ltd.
The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli matrices is shown to not be completely true. It is only true as long as the term βψ in the usual Dirac factorization of the Klein-Gordon equation is assumed to be the product of a square matrix β and a column matrix ψ. In this paper we show that there is another possibility besides this matrix product, in fact a possibility involving a matrix operation, and show that it leads to another possible expression for the Dirac equation. We show that, behind this other possible factorization is the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss several different aspects of Dirac theory using this formalism. In particular, we show that there are four different possible sets of definitions for the parity, time reversal, and charge conjugation operations for the Dirac equation
Subject: Clifford Algebra
Dirac Equation
Spinors
Clifford, Álgebra de
Dirac, Equação de
Klein-Gordon, Equação de
Teoria quântica de campos
Country: Reino Unido
Editor: Institute of Physics Publishing
Citation: European Journal Of Physics. Institute Of Physics Publishing, v. 37, n. 5, p. , 2016.
Rights: aberto
Identifier DOI: 10.1088/0143-0807/37/5/055407
Address: https://iopscience.iop.org/article/10.1088/0143-0807/37/5/055407
Date Issue: 2016
Appears in Collections:IMECC - Artigos e Outros Documentos

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