4,780 research outputs found
Solving the Constraints of General Relativity
I show in this letter that it is possible to solve some of the constraints of
the -ADM formalism for general relativity by using an approach similar
to the one introduced by Capovilla, Dell and Jacobson to solve the vector and
scalar constraints in the Ashtekar variables framework. I discuss the
advantages of using the ADM formalism and compare the result with similar
proposals for different Hamiltonian formulations of general relativity.Comment: 8 pages, LATEX, no figures, Preprint CGPG-94/11-
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
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.
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.
In-situ steel solidification imaging in continuous casting using magnetic induction tomography
: Solidification process in continuous casting is a critical part of steel production. The speed and quality of the solidification process determines the quality of final product. Computational fluid dynamics (CFD) simulations are often used to describe the process and design of its control system, but so far, there is no any tool that provides an on-line measurement of the solidification front of hot steel during the continuous casting process. This paper presents a new tool based on magnetic induction tomography (MIT) for real time monitoring of this process. The new MIT system was installed at the end of the secondary cooling chamber of a casting unit and tested during several days in a real production process. MIT is able to create an internal map of electrical conductivity of hot steel deep inside the billet. The image of electrical conductivity is then converted to temperature profile that allows the measurement of the solid, mushy and liquid layers. In this study, such a conversion is done by synchronizing in one time step the MIT measurement and the thermal map generated with the actual process parameters available at that time. The MIT results were then compared with the results obtained of the CFD and thermal modelling of the industrial process. This is the first in-situ monitoring of the interior structure during a real continuous casting.The SHELL-THICK project has received funding from EU Research Fund for Coal and Steel under grant number 709830. This study reflects only the author's views and the European Commission is not responsible for any use that may be made of the information contained therein
Reality conditions for Ashtekar variables as Dirac constraints
We show that the reality conditions to be imposed on Ashtekar variables to
recover real gravity can be implemented as second class constraints a la Dirac.
Thus, counting gravitational degrees of freedom follows accordingly. Some
constraints of the real theory turn out to be non-polynomial, regardless of the
form, polynomial or non-polynomial, taken for the reality conditions. We
comment upon the compatibility of our approach with the recently proposed Wick
transform point of view, as well as on some alternatives for dealing with such
second class constraints.Comment: 16 pages, plain LaTeX, submitted to Class. Quant. Grav. E-mail:
[email protected]
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
Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation
We examine the reduced phase space of the Barbero-Varadarajan solutions of
the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We
show that it is a finite-dimensional space due to existence of an infinite
dimensional residual gauge invariance which reduces the infinite-dimensional
space of solutions to a finite-dimensional space of gauge-inequivalent
solutions. This is in agreement with general arguments which imply that the
number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on
a torus is finite.Comment: 13 pages, Latex. More details have been included and the expression
for the finite residual gauge transformations has been worked ou
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