Local well-posedness for membranes in the light cone gauge

Details Local well-posedness for membranes in the light cone gauge Local well-posedness for membranes in the light cone gauge

2009-10-08

arxiv.org/abs/0910.1488v1

Commun.Math.Phys.301:383-410,2011

Physics

High Energy Physics

High Energy Physics - Theory

29 pages

Scientific paper

10.1007/s00220-010-1141-5

In this paper we consider the classical initial value problem for the bosonic membrane in light cone gauge. A Hamiltonian reduction gives a system with one constraint, the area preserving constraint. The Hamiltonian evolution equations corresponding to this system, however, fail to be hyperbolic. Making use of the area preserving constraint, an equivalent system of evolution equations is found, which is hyperbolic and has a well-posed initial value problem. We are thus able to solve the initial value problem for the Hamiltonian evolution equations by means of this equivalent system. We furthermore obtain a blowup criterion for the membrane evolution equations, and show, making use of the constraint, that one may achieve improved regularity estimates.

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