User:Peeter.joot: Difference between revisions

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Revision as of 18:29, 12 November 2010

I am a computer programmer for IBM and work on our DB2 product. My wikipedia contributions have mostly been in the Geometric algebra page, which is now too big and rather unencyclopedic, but still incomplete (just less so) -- much of it should be converted to a wikibook.

I've got some personal math and physics musings, including what I originally based my GA wiki contributions on, in regular latex produced pdfs available on my web page (a math and physics learning "blog"). The info on my pages does not have all the grammar and typo fixes that other wiki editors have contributed since, but does have some additional details and newer content that I omitted from the wikipedia Geometric Algebra page.

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 == sandbox ==
-===Geometric Algebra (GA) formulation===
-{{Main|Mathematical descriptions of the electromagnetic field}}
-In [[geometric algebra]], Maxwell's equations are reduced to a single equation,
-:<math> \left(\frac{1}{c}\partial_t + \boldsymbol{\nabla}\right)F = \mu_0 c J,</math><ref>Oersted Medal Lecture David Hestenes (Am. J. Phys. 71 (2), February 2003, pp. 104--121)Online:http://geocalc.clas.asu.edu/html/Oersted-ReformingTheLanguage.html</ref>
-where F and J are multivectors
-:<math> F = \bold{E} + Ic\bold{B} </math>
-and
-:<math> J = c \rho + \bold{J}.</math>
-:<math> I = \mathbf{e_x e_y e_z}\  I^2 {{=}} -1</math>
-is the unit [[pseudoscalar]] and <math>\boldsymbol{\nabla}</math>the GA spatial gradient operator acts on a vector field, such that
-:<math> \boldsymbol{\nabla}\bold{F} = \boldsymbol{\nabla} \cdot \bold{F} + I \boldsymbol{\nabla} \times \bold{F},</math>
-or, in other words,
-:<math>\text{grad}\, \mathbf{F} = \text{div}\, \mathbf{F} + I \text{curl}\, \mathbf{F}.</math>
-In [[spacetime algebra]] using the same geometric product  the equation is simply
-:<math> \nabla F = \mu_0 c J,</math>
-the spacetime derivative of the electromagnetic field is its source.  Here the (non-bold) spacetime gradient
-:<math>\nabla = \gamma^\mu \partial_\mu</math>
-is a four vector, as is the current density
-:<math>J = \gamma_{\mu} J^{\mu} = \gamma_0 c \rho + J^k \gamma_k = (c \rho + \bold{J})\gamma_0.</math>
-For a demonstration that the equations given reproduce Maxwell's equations see the main article.