Quantum and semiclassical aspects of the rigid dirac membrane with tension

We review the proposal long ago set by Dirac to model the electron as a charged membrane. A rigidity correction term involving linearly the extrinsic curvature of the worldvolume swept out by the membrane is included in the action modeling the membrane in the presence of an electromagnetic field. We analyze this model as a genuine second-order derivative theory by considering a non-trivial boundary term related to the extrinsic curvature, and which plays a relevant part in our formulation. By means of an Ostrogradski-Hamiltonian approach we observed that the theory comprises the management of both first-and second-class constraints. The effective potential which governs the membrane dynamics exhibits a minimum and, in consequence, we have a finite radius for the membrane. We show thus that our second-order approach is robust while performing a semiclassical approximation, allowing for a proper quantization. The model, due to its characteristics, may be relevant to describe brane world universes, where second-order correction terms may play an important role.