The dynamics of relativistic membranes. Reduction to 2-dimensional fluid dynamics

Abstract

We greatly simplify the light-cone gauge description of a relativistic membrane moving in Minkowski space by performing a field-dependent change of variables which allows the explicit solution of all constraints and a Hamiltonian reduction to a SO(1, 3) invariant 2 + 1-dimensional theory of isentropic gas dynamics, where the pressure is inversely proportional to (minus) the mass-density. Simple expressions for the generators of the Poincaré group are given. We also find a generalized Lax pair which involves as a novel feature complex conjugation. The extension to the supersymmetric case, as well as to higher-dimensional minimal surfaces of codimension one is briefly mentioned.

Letter: Density Perturbations in a Universe Dominated by the Chaplygin Gas

“…This exotic fluid has an interesting origin. Taking the NambuGoto action of string theory, the Chaplygin fluid appears after considering d-branes in a 1 e-mail: fabris@cce.ufes.br 2 e-mail: sergio@cce.ufes.br 3 e-mail: patricia.ilus@bol.com.br d + 2 dimensional space-time, in the light cone gauge [6]. In this case, the Nambu action reduces to [7] …”

“…Introducing in equations (4,5,6) the quantities ρ = ρ 0 + δρ, v = v 0 + δ v, p = p 0 + δp and φ = φ 0 + δφ, where each quantity has been expressed as a sum of the background solution plus a small perturbation, we can combine the resulting perturbed equation in order to obtain an unique differential equation…”

Clebsch parameterization from the symplectic point of view

“…In Ref. [2], the authors Afterwards, Bazeia and Jackiw [3], found the solutions of this Galileo invariant system that are in connection with the solutions of the relativistic D-brane system. In particular, these works clarify the presence of a hidden dynamical Poincaré symmetry on the d-dimensional fluid mechanics.…”

“…Recently, fluid mechanics [1] has attracted a huge attention to theoretical physicists [2,3] due to the investigate of how some instances of the classical theory are related to D-branes and how this relation explains some integrability properties of several models. In Ref.…”

Two-dimensional solutions for Born-Infeld fields

“…It descends from the Nambu-Goto action for a string in 2+1 dimensions when a proper parametrization is chosen [1]. Besides, its solutions can be mapped into solutions of the Galileoinvariant Chaplygin gas in 1+1 dimensions, since Chaplygin gas is another descendent of the Nambu-Goto action [2,3]. Born-Infeld equation (1) also takes part in Born-Infeld electrodynamics [4,5] when electromagnetic waves depending just on two variables are considered.…”