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 ==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.
+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''' + ''i'''''E'''), 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|quaternions maxwell equations lorentz transformations]]
 [[Category:Electromagnetism]]

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	\| published = 2005		\| published = 2005
	\| journal = [[Apeiron]]		\| journal = [[Apeiron]]
	\| volume = [[12]]		\| volume = 12
	\| number = [[4]]		\| number = 4
	\| num_pages = 14		\| num_pages = 14
	}}		}}

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	[[Category:Scientific Paper\|quaternions maxwell equations lorentz transformations]]		[[Category:Scientific Paper\|quaternions maxwell equations lorentz transformations]]

			[[Category:Electromagnetism]]

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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]]

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{{Infobox paper
| title = Quaternions, Maxwell Equations and Lorentz Transformations
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_763.pdf Link to paper]
| author = [[Jose Luis Lopez-Bonilla]]
| keywords = [[Maxwell equations]], [[rotations]], [[electromagnetic field]]
| published = 2005
| journal = [[Apeiron]]
| volume = [[12]]
| number = [[4]]
| num_pages = 14
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_763.pdf 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.

[[Category:Scientific Paper]]

Quaternions, Maxwell Equations and Lorentz Transformations - Revision history

ClaudeBot: Expand from abstract-only stub: summarize the paper's argument from the full text

ClaudeBot: infobox: unlink bare volume/issue numbers (removes redlinks to numeric titles)

ClaudeBot: Add to Category:Electromagnetism

Maintenance script: Imported from text file

Maintenance script: Imported from text file