5,697 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
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.
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
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.
Uniqueness of the Fock representation of the Gowdy and models
After a suitable gauge fixing, the local gravitational degrees of freedom of
the Gowdy and cosmologies are encoded in an axisymmetric
field on the sphere . Recently, it has been shown that a standard field
parametrization of these reduced models admits no Fock quantization with a
unitary dynamics. This lack of unitarity is surpassed by a convenient
redefinition of the field and the choice of an adequate complex structure. The
result is a Fock quantization where both the dynamics and the SO(3)-symmetries
of the field equations are unitarily implemented. The present work proves that
this Fock representation is in fact unique inasmuch as, up to equivalence,
there exists no other possible choice of SO(3)-invariant complex structure
leading to a unitary implementation of the time evolution.Comment: 10 pages, minor changes, version accepted for publication in
Classical and Quantum Gravit
The structure of the distortion free-energy density in nematics: second-order elasticity and surface terms
Alignment transition in a nematic liquid crystal due to field-induced breaking of anchoring
We report on the alignment transition of a nematic liquid crystal from
initially homeotropic to quasi-planar due to field-induced anchoring breaking.
The initial homeotropic alignment is achieved by Langmuir-Blodgett monolayers.
In this geometry the anchoring strength can be evaluated by the Frederiks
transition technique. Applying an electric field above a certain threshold
provokes turbulent states denoted DSM1 and DSM2. While DSM1 does not affect the
anchoring, DSM2 breaks the coupling between the surface and the liquid crystal:
switching off the field from a DSM2 state does not immediately restore the
homeotropic alignment. Instead, we obtain a quasi-planar metastable alignment.
The cell thickness dependence for the transition is related to theComment: 7 pages, LaTeX2e article, 4 figures, 7 EPS files, added references,
accepted for publication in Europhysics Letter
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