199 research outputs found
Branes as solutions of gauge theories in gravitational field
The idea of the Gauss map is unified with the concept of branes as
hypersurfaces embedded into -dimensional Minkowski space. The map introduces
new generalized coordinates of branes alternative to their world vectors
and identified with the gauge and other massless fields. In these
coordinates the Dirac -branes realize extremals of the Euler-Lagrange
equations of motion of a -dimensional gauge-invariant action
in a gravitational backgroundComment: 21 pages. Published version: extended Introduction, additional
clarifications and comments, new references and improved styl
U(1)-invariant membranes: the geometric formulation, Abel and pendulum differential equations
The geometric approach to study the dynamics of U(1)-invariant membranes is
developed. The approach reveals an important role of the Abel nonlinear
differential equation of the first type with variable coefficients depending on
time and one of the membrane extendedness parameters. The general solution of
the Abel equation is constructed. Exact solutions of the whole system of
membrane equations in the D=5 Minkowski space-time are found and classified. It
is shown that if the radial component of the membrane world vector is only time
dependent then the dynamics is described by the pendulum equation.Comment: 19 pages, v3 published versio
- …