5,036 research outputs found
SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter
An so(4,C)-covariant hamiltonian formulation of a family of generalized
Hilbert-Palatini actions depending on a parameter (the so called Immirzi
parameter) is developed. It encompasses the Ashtekar-Barbero gravity which
serves as a basis of quantum loop gravity. Dirac quantization of this system is
constructed. Next we study dependence of the quantum system on the Immirzi
parameter. The path integral quantization shows no dependence on it. A way to
modify the loop approach in the accordance with the formalism developed here is
briefly outlined.Comment: 14 pages, LATEX; minor changes; misprints corrected; commutator of
two secondary second class constraints correcte
Real Ashtekar Variables for Lorentzian Signature Space-times
I suggest in this letter a new strategy to attack the problem of the reality
conditions in the Ashtekar approach to classical and quantum general
relativity. By writing a modified Hamiltonian constraint in the usual
Yang-Mills phase space I show that it is possible to describe space-times with
Lorentzian signature without the introduction of complex variables. All the
features of the Ashtekar formalism related to the geometrical nature of the new
variables are retained; in particular, it is still possible, in principle, to
use the loop variables approach in the passage to the quantum theory. The key
issue in the new formulation is how to deal with the more complicated
Hamiltonian constraint that must be used in order to avoid the introduction of
complex fields.Comment: 10 pages, LATEX, Preprint CGPG-94/10-
The Husain-Kuchar Model: Time Variables and Non-degenerate Metrics
We study the Husain-Kuchar model by introducing a new action principle
similar to the self-dual action used in the Ashtekar variables approach to
Quantum Gravity. This new action has several interesting features; among them,
the presence of a scalar time variable that allows the definition of geometric
observables without adding new degrees of freedom, the appearance of a natural
non-degenerate four-metric and the possibility of coupling ordinary matter.Comment: LaTeX, 22 pages, accepted for publication in Phys. Rev.
Weak decay processes in pre-supernova core evolution within the gross theory
The beta decay and electron capture rates are of fundamental importance in the evolution of massive stars in a pre-supernova core. The beta decay process gives its contribution by emitting electrons in the plasma of the stellar core, thereby increasing pressure, which in turn increases the temperature. From the other side, the electron capture removes free electrons from the plasma of the star core contributing to the reduction of pressure and temperature. In this work we calculate the beta decay and electron capture rates in stellar conditions for 63 nuclei of relevance in the pre-supernova stage, employing Gross Theory as the nuclear model. We use the abundances calculated with the Saha equations in the hypothesis of nuclear statistical equilibrium to evaluate the time derivative of the fraction of electrons. Our results are compared with other evaluations available in the literature. They have shown to be one order less or equal than the calculated within other models. Our results indicate that these differences may influence the evolution of the star in the later stages of pre-supernova. © 2014. The American Astronomical Society. All rights reserved..Fil: Ferreira, R. C.. Universidade Estadual Do Sudoeste Da BahĂa; BrasilFil: Dimarco, A. J.. Universidade Estadual de Santa Cruz, BahĂa, Brasil; BrasilFil: Samana, Arturo Rodolfo. Universidade Estadual de Santa Cruz, BahĂa, Brasil; BrasilFil: Barbero, CĂ©sar Alberto. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - La Plata. Instituto de FĂsica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de FĂsica La Plata; Argentin
BF Actions for the Husain-Kuchar Model
We show that the Husain-Kuchar model can be described in the framework of BF
theories. This is a first step towards its quantization by standard
perturbative QFT techniques or the spin-foam formalism introduced in the
space-time description of General Relativity and other diff-invariant theories.
The actions that we will consider are similar to the ones describing the
BF-Yang-Mills model and some mass generating mechanisms for gauge fields. We
will also discuss the role of diffeomorphisms in the new formulations that we
propose.Comment: 21 pages (in DIN A4 format), minor typos corrected; to appear in
Phys. Rev.
Hilbert space structure of covariant loop quantum gravity
We investigate the Hilbert space in the Lorentz covariant approach to loop
quantum gravity. We restrict ourselves to the space where all area operators
are simultaneously diagonalizable, assuming that it exists. In this sector
quantum states are realized by a generalization of spin network states based on
Lorentz Wilson lines projected on irreducible representations of an SO(3)
subgroup. The problem of infinite dimensionality of the unitary Lorentz
representations is absent due to this projection. Nevertheless, the projection
preserves the Lorentz covariance of the Wilson lines so that the symmetry is
not broken. Under certain conditions the states can be thought as functions on
a homogeneous space. We define the inner product as an integral over this
space. With respect to this inner product the spin networks form an orthonormal
basis in the investigated sector. We argue that it is the only relevant part of
a larger state space arising in the approach. The problem of the
noncommutativity of the Lorentz connection is solved by restriction to the
simple representations. The resulting structure shows similarities with the
spin foam approach.Comment: 20 pages, RevTE
Global controllability tests for geometric hybrid control systems
Hybrid systems are characterized by having an interaction between continuous
dynamics and discrete events. The contribution of this paper is to provide
hybrid systems with a novel geometric formulation so that controls can be
added. Using this framework we describe some new global controllability tests
for hybrid control systems exploiting the geometry and the topology of the set
of jump points, where the instantaneous change of dynamics take place.
Controllability is understood as the existence of a feasible trajectory for the
system joining any two given points. As a result we describe examples where
none of the continuous control systems are controllable, but the associated
hybrid system is controllable because of the characteristics of the jump set.Comment: 27 pages, 5 figure
Evolution Operators for Linearly Polarized Two-Killing Cosmological Models
We give a general procedure to obtain non perturbative evolution operators in
closed form for quantized linearly polarized two Killing vector reductions of
general relativity with a cosmological interpretation. We study the
representation of these operators in Fock spaces and discuss in detail the
conditions leading to unitary evolutions.Comment: Accepted for publication in Physical Review
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