45 research outputs found
Adjoint operators, gauge invariant perturbations, and covariant symplectic structure for black holes in string theory
Expressions for the general and complete perturbations in terms of Debye
potentials of static charged black holes in string theory, valid for curvature
below the Planck scale, are derived starting from a decoupled set of equations
and using Wald's method of adjoint operators. Our results cover both extremal
and nonextremal black holes and are valid for arbitrary values of the dilaton
coupling parameter. The decoupled set is obtained using the Newman-Penrose
formulation of the Einstein-Maxwell-dilaton theory and involves naturally field
quantities invariant under both ordinary gauge transformations of the
electromagnetic potential perturbations and infinitesimal rotations of the
perturbed tetrad. Furthermore, using the recent pointed out relationship
between adjoint operators and conserved currents, a local continuity law for
the field perturbations in terms of the potentials is also obtained. It is
shown that such continuity equation implies the existence of conserved
quantities and of a covariant symplectic structure on the phase space. Future
extensions of the present results are discussed.Comment: LaTeX, 36 pages, submitted to J. Math. Phys. (2002
On the symplectic structures for geometrical theories
We present a new approach for constructing covariant symplectic structures
for geometrical theories, based on the concept of adjoint operators. Such
geometric structures emerge by direct exterior derivation of underlying
symplectic potentials. Differences and similarities with other approaches and
future applications are discussed.Comment: LaTeX, 12 page
Identically closed two-form for covariant phase space quantization of Dirac-Nambu-Goto p-branes in a curved spacetime
Using a fully covariant formalism given by Carter for the deformation
dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved
background, it is proved that the corresponding Witten's phase space is endowed
with a covariant symplectic structure, which can serve as a starting point for
a phase space quantization of such objects. Some open questions for further
research are outlined.Comment: LaTeX, 8 pages, to be published in Phys. Lett. B. (2002
Global symplectic potentials on the Witten covariant phase space for bosonic extendons
It is proved that the projections of the deformation vector field, normal and
tangential to the worldsheet manifold swept out by Dirac-Nambu-Goto bosonic
extendons propagating in a curved background, play the role of {\it global}
symplectic potentials on the corresponding Witten covariant phase space. It is
also proved that the {\it presymplectic} structure obtained from such
potentials by direct exterior derivation, has not components tangent to the
action of the relevant diffeomorphisms group of the theory.Comment: LaTeX, 8 pages, submitted to Phys. Lett. B. (2002
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