Quaternions, Maxwell Equations and Lorentz Transformations: Difference between revisions
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In this work: a) We show that the invariance of the Maxwell equations under duality rotations brings into scene to the complex vector (''c B iE'' ? ?), whose components allow to construct a quaternionic equation for the electromagnetic field in vacuo. b) For any analytic function f of the complex variable z, it is possible to prove that is a Debye potential for itself, which permits to reformulate the corresponding Cauchy-Riemann relations. Here we show that the Fueter conditions- when z is a quaternion- also accept a similar reformulation and a very compact quaternionic expression. c) We exhibit how the rotations in three and four dimensions can be described through a complex matrix relation or equivalently by a quaternionic formula. | In this work: a) We show that the invariance of the Maxwell equations under duality rotations brings into scene to the complex vector (''c B iE'' ? ?), whose components allow to construct a quaternionic equation for the electromagnetic field in vacuo. b) For any analytic function f of the complex variable z, it is possible to prove that is a Debye potential for itself, which permits to reformulate the corresponding Cauchy-Riemann relations. Here we show that the Fueter conditions- when z is a quaternion- also accept a similar reformulation and a very compact quaternionic expression. c) We exhibit how the rotations in three and four dimensions can be described through a complex matrix relation or equivalently by a quaternionic formula. | ||
[[Category:Scientific Paper]] | [[Category:Scientific Paper|quaternions maxwell equations lorentz transformations]] | ||
Latest revision as of 12:57, 1 January 2017
| Scientific Paper | |
|---|---|
| Title | Quaternions, Maxwell Equations and Lorentz Transformations |
| Read in full | Link to paper |
| Author(s) | Jose Luis Lopez-Bonilla |
| Keywords | Maxwell equations, rotations, electromagnetic field |
| Published | 2005 |
| Journal | Apeiron |
| Volume | 12 |
| Number | 4 |
| No. of pages | 14 |
Read the full paper here
Abstract
In this work: a) We show that the invariance of the Maxwell equations under duality rotations brings into scene to the complex vector (c B iE ? ?), whose components allow to construct a quaternionic equation for the electromagnetic field in vacuo. b) For any analytic function f of the complex variable z, it is possible to prove that is a Debye potential for itself, which permits to reformulate the corresponding Cauchy-Riemann relations. Here we show that the Fueter conditions- when z is a quaternion- also accept a similar reformulation and a very compact quaternionic expression. c) We exhibit how the rotations in three and four dimensions can be described through a complex matrix relation or equivalently by a quaternionic formula.