52 research outputs found
The Euler characteristic and the first Chern number in the covariant phase space formulation of string theory
Using a covariant description of the geometry of deformations for extendons,
it is shown that the topological corrections for the string action associated
with the Euler characteristic and the first Chern number of the normal bundle
of the worldsheet, although do not give dynamics to the string, modify the
symplectic properties of the covariant phase space of the theory. Future
extensions of the present results are outlined.Comment: 12 page
Yang-Mills theory a la string
A surface of codimension higher than one embedded in an ambient space
possesses a connection associated with the rotational freedom of its normal
vector fields. We examine the Yang-Mills functional associated with this
connection. The theory it defines differs from Yang-Mills theory in that it is
a theory of surfaces. We focus, in particular, on the Euler-Lagrange equations
describing this surface, introducing a framework which throws light on their
relationship to the Yang-Mills equations.Comment: 7 page
Supertubes versus superconducting tubes
In this paper we show the relationship between cylindrical D2-branes and
cylindrical superconducting membranes described by a generic effective action
at the bosonic level. In the first case the extended objects considered, arose
as blown up type IIA superstrings to D2-branes, named supertubes. In the second
one, the cosmological objects arose from some sort of field theories. The
Dirac-Born-Infeld action describing supertubes is shown to be equivalent to the
generic effective action describing superconducting membranes via a special
transformation.Comment: Version with minor text changes with respect to the already publishe
Hamiltonian Frenet-Serret dynamics
The Hamiltonian formulation of the dynamics of a relativistic particle
described by a higher-derivative action that depends both on the first and the
second Frenet-Serret curvatures is considered from a geometrical perspective.
We demonstrate how reparametrization covariant dynamical variables and their
projections onto the Frenet-Serret frame can be exploited to provide not only a
significant simplification of but also novel insights into the canonical
analysis. The constraint algebra and the Hamiltonian equations of motion are
written down and a geometrical interpretation is provided for the canonical
variables.Comment: Latex file, 14 pages, no figures. Revised version to appear in Class.
Quant. Gra
Auxiliary fields in the geometrical relativistic particle dynamics
We describe how to construct the dynamics of relativistic particles
following, either timelike or null curves, by means of an auxiliary variables
method instead of the standard theory of deformations for curves. There are
interesting physical particle models governed by actions that involve higher
order derivatives of the embedding functions of the worldline. We point out
that the mechanical content of such models can be extracted wisely from a lower
order action, which can be performed by implementing in the action a finite
number of constraints that involve the geometrical relationship structures
inherent to a curve and by using a covariant formalism. We emphasize our
approach for null curves. For such systems, the natural time parameter is a
pseudo-arclength whose properties resemble those of the standard proper time.
We illustrate the formalism by applying it to some models for relativistic
particles.Comment: 13 pages, no figure
Bose-Einstein condensate dark matter phase transition from finite temperature symmetry breaking of Klein-Gordon fields
In this paper the thermal evolution of scalar field dark matter particles at
finite cosmological temperatures is studied. Starting with a real scalar field
in a thermal bath and using the one loop quantum corrections potential, we
rewrite Klein-Gordon's (KG) equation in its hydrodynamical representation and
study the phase transition of this scalar field due to a Z_2 symmetry breaking
of its potential. A very general version of a nonlinear Schr\"odinger equation
is obtained. When introducing Madelung's representation, the continuity and
momentum equations for a non-ideal SFDM fluid are formulated, and the
cosmological scenario with the SFDM described in analogy to an imperfect fluid
is then considered where dissipative contributions are obtained in a natural
way.Additional terms appear compared to those obtained in the classical version
commonly used to describe the \LambdaCDM model, i.e., the ideal fluid. The
equations and parameters that characterize the physical properties of the
system such as its energy, momentum and viscous flow are related to the
temperature of the system, scale factor, Hubble's expansion parameter and the
matter energy density. Finally, some details on how galaxy halos and smaller
structures might be able to form by condensation of this SF are given.Comment: Substantial changes have been made to the paper, following the
referees recommendations. 16 pages. Published in Classical and Quantum
Gravit
Noether Currents for Bosonic Branes
We consider a relativistic brane propagating in Minkowski spacetime described
by any action which is local in its worldvolume geometry. We examine the
conservation laws associated with the Poincar\'e symmetry of the background
from a worldvolume geometrical point of the view. These laws are exploited to
explore the structure of the equations of motion. General expressions are
provided for both the linear and angular momentum for any action depending on
the worldvolume extrinsic curvature. The conservation laws are examined in
perturbation theory. It is shown how non-trivial solutions with vanishing
energy-momentum can be constructed in higher order theories. Finally,
subtleties associated with boundary terms are examined in the context of the
brane Einstein-Hilbert action.Comment: 33 pages, Latex. Published in Annals of Physics 279, 126, 200
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