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Complementing the Lagrangian Density of the E. M. Field and the Surface Integral of the p-v Vector Product

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DOI: 10.4236/am.2011.22024    5,118 Downloads   9,065 Views  
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ABSTRACT

Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equations of the complete Lagrangian density. The 4 × 4 transformation matrix introduces newly defined vector products. In a Theorem the surface integral of one of the newly defined vector products is shown to be reduced to a line integral.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Rashid, "Complementing the Lagrangian Density of the E. M. Field and the Surface Integral of the p-v Vector Product," Applied Mathematics, Vol. 2 No. 2, 2011, pp. 225-229. doi: 10.4236/am.2011.22024.

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