Brane Variation Dirac Style

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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7 pages, 1 eps figure, paper revised

Scientific paper

10.1088/0264-9381/21/6/001

Dirac's method for variations of a brane embedded in co-dimension one is demonstrated. The variation in the location of the brane invokes a rest frame formulation of the 'sandwiched' brane action. We first demonstrate the necessity of this method by re-deriving Snell's law. Second, we apply the method to a general $N$-dimensional brane embedded in co-dimension one bulk in the presence of gravity. We re-derive the brane equations: (i) Israel junction condition, (ii) Energy/momentum conservation on the brane, and (iii) Geodetic-type equation for the brane.

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