2,134 research outputs found
Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories
The most general action, quadratic in the B fields as well as in the
curvature F, having SO(3,1) or SO(4) as the internal gauge group for a
four-dimensional BF theory is presented and its symplectic geometry is
displayed. It is shown that the space of solutions to the equations of motion
for the BF theory can be endowed with symplectic structures alternative to the
usual one. The analysis also includes topological terms and cosmological
constant. The implications of this fact for gravity are briefly discussed.Comment: 13 pages, LaTeX file, no figure
Tidal Disruption Flares: The Accretion Disk Phase
The evolution of an accretion disk, formed as a consequence of the disruption
of a star by a black hole, is followed by solving numerically the hydrodynamic
equations. The present investigation aims to study the dependence of resulting
light curves on dynamical and physical properties of such a transient disk
during its existence. One of main results derived from our simulations is that
black body fits of X-ray data tend to overestimate the true mean disk
temperature. The temperature derived from black body fits should be identified
with the color X-ray temperature rather than the average value derived from the
true temperature distribution along the disk. The time interval between the
beginning of the circularization of the bound debris and the beginning of the
accretion process by the black hole is determined by the viscous timescale,
which fixes also the raising part of the resulting light curve. The luminosity
peak coincides with the beginning of matter accretion by the black hole and the
late evolution of the light curve depends on the evolution of the debris
fallback rate. Peak bolometric luminosities are in the range 10^45-10^46 erg
s^-1 whereas peak luminosities in soft X-rays (0.2-2.0 keV) are typically one
order of magnitude lower. The timescale derived from our preferred models for
the flare luminosity to decay by two orders of magnitude is about 3-4 years.
Predicted soft X-ray light curves were fitted to data on galaxies in which a
variable X-ray emission, related to tidal events, was detected.Comment: 14 pages, 11 figures, Accepted for publication in Ap
Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures
A proposal for the Hamilton-Jacobi theory in the context of the covariant
formulation of Hamiltonian systems is done. The current approach consists in
applying Dirac's method to the corresponding action which implies the inclusion
of second-class constraints in the formalism which are handled using the
procedure of Rothe and Scholtz recently reported. The current method is applied
to the nonrelativistic two-dimensional isotropic harmonic oscillator employing
the various symplectic structures for this dynamical system recently reported.Comment: 17 pages, no figure
Fermion mass gap in the loop representation of quantum gravity
An essential step towards the identification of a fermion mass generation
mechanism at Planck scale is to analyse massive fermions in a given quantum
gravity framework. In this letter the two mass terms entering the Hamiltonian
constraint for the Einstein-Majorana system are studied in the loop
representation of quantum gravity and fermions. One resembles a bare mass gap
because it is not zero for states with zero (fermion) kinetic energy as
opposite to the other that is interpreted as `dressing' the mass. The former
contribution originates from (at least) triple intersections of the loop states
acted on whilst the latter is traced back to every couple of coinciding end
points, where fermions sit. Thus, fermion mass terms get encoded in the
combinatorics of loop states. At last the possibility is discussed of relating
fermion masses to the topology of space.Comment: 15 pages, Latex file, no figures. To be published in Classical and
Quantum Gravit
Linear constraints from generally covariant systems with quadratic constraints
How to make compatible both boundary and gauge conditions for generally
covariant theories using the gauge symmetry generated by first class
constraints is studied. This approach employs finite gauge transformations in
contrast with previous works which use infinitesimal ones. Two kinds of
variational principles are taken into account; the first one features
non-gauge-invariant actions whereas the second includes fully gauge-invariant
actions. Furthermore, it is shown that it is possible to rewrite fully
gauge-invariant actions featuring first class constraints quadratic in the
momenta into first class constraints linear in the momenta (and homogeneous in
some cases) due to the full gauge invariance of their actions. This shows that
the gauge symmetry present in generally covariant theories having first class
constraints quadratic in the momenta is not of a different kind with respect to
the one of theories with first class constraints linear in the momenta if fully
gauge-invariant actions are taken into account for the former theories. These
ideas are implemented for the parametrized relativistic free particle,
parametrized harmonic oscillator, and the SL(2,R) model.Comment: Latex file, revtex4, 18 pages, no figures. This version includes the
corrections to many misprints of v1 and also the ones of the published
version. The conceptual and technical parts of the paper are not altere
A topological limit of gravity admitting an SU(2) connection formulation
We study the Hamiltonian formulation of the generally covariant theory
defined by the Lagrangian 4-form L=e_I e_J F^{IJ}(\omega) where e^I is a tetrad
field and F^{IJ} is the curvature of a Lorentz connection \omega^{IJ}. This
theory can be thought of as the limit of the Holst action for gravity for the
Newton constant G goes to infinity and Immirzi parameter goes to zero, while
keeping their product fixed. This theory has for a long time been conjectured
to be topological. We prove this statement both in the covariant phase space
formulation as well as in the standard Dirac formulation. In the time gauge,
the unconstrained phase space of theory admits an SU(2) connection formulation
which makes it isomorphic to the unconstrained phase space of gravity in terms
of Ashtekar-Barbero variables. Among possible physical applications, we argue
that the quantization of this topological theory might shed new light on the
nature of the degrees of freedom that are responsible for black entropy in loop
quantum gravity.Comment: Appendix added where moldels leading to boundary degrees of freedom
are constructed. This version will appear in PRD
Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter
We perform the Lorentz-covariant Hamiltonian analysis of two Lagrangian
action principles that describe general relativity as a constrained BF theory
and that include the Immirzi parameter. The relation between these two
Lagrangian actions has been already studied through a map among the fields
involved. The main difference between these is the way the Immirzi parameter is
included, since in one of them the Immirzi parameter is included explicitly in
the BF terms, whereas in the other (the CMPR action) it is in the constraint on
the B fields. In this work we continue the analysis of their relationship but
at the Hamiltonian level. Particularly, we are interested in seeing how the
above difference appears in the constraint structure of both action principles.
We find that they both possess the same number of first-class and second-class
constraints and satisfy a very similar (off-shell) Poisson-bracket algebra on
account of the type of canonical variables employed. The two algebras can be
transformed into each other by making a suitable change of variablesComment: LaTeX file, no figure
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