Quantum charged rigid membrane

Abstract

The early Dirac proposal to model the electron as a charged membrane is\nreviewed. A rigidity term, instead of the natural membrane tension, involving\nlinearly the extrinsic curvature of the worldvolume swept out by the membrane\nis considered in the action modeling the bubble in the presence of an\nelectromagnetic field. We set up this model as a genuine second-order\nderivative theory by considering a non-trivial boundary term which plays a\nrelevant part in our formulation. The Lagrangian in question is linear in the\nbubble acceleration and by means of the Ostrogradski-Hamiltonian approach we\nobserved that the theory comprises the management of both first- and\nsecond-class constraints. We show thus that our second-order approach is robust\nallowing for a proper quantization. We found an effective quantum potential\nwhich permits to compute bounded states for the system. We comment on the\npossibility of describing brane world universes by invoking this kind of\nsecond-order correction terms.\n