dorsal/arxiv
View SchemaLorentz Invariant Majorana Formulation of the Field Equations and Dirac-like Equation for the Free Photon
| Authors | Tomislav Ivezic |
|---|---|
| Categories | |
| ArXiv ID | physics/0605030 |
| URL | https://arxiv.org/abs/physics/0605030 |
| Journal | EJTP 10 (2006) 131-142 |
Abstract
In this paper we present a new geometric formulation (Clifford algebra formalism) of the field equations, which is independent of the reference frame and of the chosen system of coordinates in it. This formulation deals with the complex 1-vector $\Psi =E-icB$ ($i$ is the unit imaginary), which is four-dimensional (4D) geometric generalization of Majorana's complex 3D quantity $\mathbf{\Psi}=\mathbf{E}-ic\mathbf{B}$. When the sources are absent the field equations with the complex $\Psi $ become Dirac-like relativistic wave equations for the free photon. In the frame of ``fiducial'' observers (the observers who measure fields are at rest) and in the standard basis the component form of the field equations with 4D $\Psi $ reproduces the component form of Majorana-Maxwell equations with 3D field $\mathbf{\Psi}$. The important differences between the approach with the 4D $\Psi $ and that one with the 3D $\mathbf{\Psi}$ are discussed.
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"abstract": "In this paper we present a new geometric formulation (Clifford algebra\nformalism) of the field equations, which is independent of the reference frame\nand of the chosen system of coordinates in it. This formulation deals with the\ncomplex 1-vector $\\Psi =E-icB$ ($i$ is the unit imaginary), which is\nfour-dimensional (4D) geometric generalization of Majorana\u0027s complex 3D\nquantity $\\mathbf{\\Psi}=\\mathbf{E}-ic\\mathbf{B}$. When the sources are absent\nthe field equations with the complex $\\Psi $ become Dirac-like relativistic\nwave equations for the free photon. In the frame of ``fiducial\u0027\u0027 observers (the\nobservers who measure fields are at rest) and in the standard basis the\ncomponent form of the field equations with 4D $\\Psi $ reproduces the component\nform of Majorana-Maxwell equations with 3D field $\\mathbf{\\Psi}$. The important\ndifferences between the approach with the 4D $\\Psi $ and that one with the 3D\n$\\mathbf{\\Psi}$ are discussed.",
"arxiv_id": "physics/0605030",
"authors": [
"Tomislav Ivezic"
],
"categories": [
"physics.gen-ph"
],
"journal_ref": "EJTP 10 (2006) 131-142",
"title": "Lorentz Invariant Majorana Formulation of the Field Equations and Dirac-like Equation for the Free Photon",
"url": "https://arxiv.org/abs/physics/0605030"
},
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