Brane Variation Dirac Style

Abstract

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.

7 pages, 1 eps figure, paper revised

References in corpus (2)

• Generic junction conditions in brane-world scenarios
• Doubly covariant action principle of singular hypersurfaces in general relativity and scalar-tensor theories

Cited by in corpus (4)

• Dirac Relaxation of the Israel Junction Conditions: Unified Randall-Sundrum Brane Theory
• Lagrangian Brane Dynamics in General Relativity and Einstein-Gauss-Bonnet Gravity
• Unified Brane Gravity: Cosmological Dark Matter from Scale Dependent Newton Constant
• Dynamics of the universe as a "test 3-brane" in a 5D bulk