Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations

Details Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations

2003-08-12

arxiv.org/abs/hep-th/0308079v1

J.Math.Phys. 44 (2003) 5888-5901

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX file, 16 pages

Scientific paper

10.1063/1.1625891

The main focus of the present work is to study the Feynman's proof of the Maxwell equations using the NC geometry framework. To accomplish this task, we consider two kinds of noncommutativity formulations going along the same lines as Feynman's approach. This allows us to go beyond the standard case and discover non-trivial results. In fact, while the first formulation gives rise to the static Maxwell equations, the second formulation is based on the following assumption $m[x_{j},\dot{x_{k}}]=i\hbar \delta_{jk}+im\theta_{jk}f.$ The results extracted from the second formulation are more significant since they are associated to a non trivial $\theta $-extension of the Bianchi-set of Maxwell equations. We find $div_{\theta}B=\eta_{\theta}$ and $\frac{\partial B_{s}}{\partial t}+\epsilon_{kjs}\frac{\partial E_{j}}{\partial x_{k}}=A_{1}\frac{d^{2}f}{dt^{2}}+A_{2}\frac{df}{dt}+A_{3},$ where $\eta_{\theta}$, $A_{1}$, $A_{2}$ and $A_{3}$ are local functions depending on the NC $\theta $-parameter. The novelty of this proof in the NC space is revealed notably at the level of the corrections brought to the previous Maxwell equations. These corrections correspond essentially to the possibility of existence of magnetic charges sources that we can associate to the magnetic monopole since $div_{\theta}B=\eta_{\theta}$ is not vanishing in general.

Affiliated with

Also associated with

No associations

Rating

Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-2428