42,311 research outputs found
On well-defined kinematic metric functions
This paper presents both formal as well as practical well-definedness conditions for kinematic metric functions. To formulate these conditions, we introduce an intrinsic definition of a rigid body's configuration space. Based on this definition, the principle of objectivity is introduced to derive a formal condition for well-definedness of kinematic metric functions, as well as to gain physical insight into left, right and bi-invariances on the Lie group SE(3). We then relate the abstract notion of objectivity to the more intuitive notion of frame-invariance, and show that frame-invariance can be used as a practical condition for determining objective functions. Examples demonstrate the utility of objectivity and frame-invariance
Complementarity of Kinematics and Geometry in General Relativity Theory
Relations between kinematics, geometry and law of reference frame motion are
considered. We show, that kinematical tensors define geometry up to a space
functional arbitrariness when integrability condition for spin tensor is
satisfied. Some aspects of geometrization principle and geometrical
conventionalism of Poincare are discussed in a light of the obtained results.Comment: The paper is developed version of talk, presented at the conference
RusGrav-2010 (June 2010, Moscow), submitted to GR
Kinematic space for conical defects
Kinematic space can be used as an intermediate step in the AdS/CFT dictionary
and lends itself naturally to the description of diffeomorphism invariant
quantities. From the bulk it has been defined as the space of boundary anchored
geodesics, and from the boundary as the space of pairs of CFT points. When the
bulk is not globally AdS the appearance of non-minimal geodesics leads to
ambiguities in these definitions. In this work conical defect spacetimes are
considered as an example where non-minimal geodesics are common. From the bulk
it is found that the conical defect kinematic space can be obtained from the
AdS kinematic space by the same quotient under which one obtains the defect
from AdS. The resulting kinematic space is one of many equivalent
fundamental regions. From the boundary the conical defect kinematic space can
be determined by breaking up OPE blocks into contributions from individual bulk
geodesics. A duality is established between partial OPE blocks and bulk fields
integrated over individual geodesics, minimal or non-minimal.Comment: 29 pages, 9 figures. As published in JHE
A proposal for analyzing the classical limit of kinematic loop gravity
We analyze the classical limit of kinematic loop quantum gravity in which the
diffeomorphism and hamiltonian constraints are ignored. We show that there are
no quantum states in which the primary variables of the loop approach, namely
the SU(2) holonomies along {\em all} possible loops, approximate their
classical counterparts. At most a countable number of loops must be specified.
To preserve spatial covariance, we choose this set of loops to be based on
physical lattices specified by the quasi-classical states themselves. We
construct ``macroscopic'' operators based on such lattices and propose that
these operators be used to analyze the classical limit. Thus, our aim is to
approximate classical data using states in which appropriate macroscopic
operators have low quantum fluctuations.
Although, in principle, the holonomies of `large' loops on these lattices
could be used to analyze the classical limit, we argue that it may be simpler
to base the analysis on an alternate set of ``flux'' based operators. We
explicitly construct candidate quasi-classical states in 2 spatial dimensions
and indicate how these constructions may generalize to 3d. We discuss the less
robust aspects of our proposal with a view towards possible modifications.
Finally, we show that our proposal also applies to the diffeomorphism invariant
Rovelli model which couples a matter reference system to the Hussain Kucha{\v
r} model.Comment: Replaced with substantially revised versio
On the resolution of the big bang singularity in isotropic Loop Quantum Cosmology
In contrast to previous work in the field, we construct the Loop Quantum
Cosmology (LQC) of the flat isotropic model with a massless scalar field in the
absence of higher order curvature corrections to the gravitational part of the
Hamiltonian constraint. The matter part of the constraint contains the inverse
triad operator which can be quantized with or without the use of a Thiemann-
like procedure. With the latter choice, we show that the LQC quantization is
identical to that of the standard Wheeler DeWitt theory (WDW) wherein there is
no singularity resolution. We argue that the former choice leads to singularity
resolution in the sense of a well defined, regular (backward) evolution through
and beyond the epoch where the size of the universe vanishes.
Our work along with that of the seminal work of Ashtekar, Pawlowski and Singh
(APS) clarifies the role, in singularity resolution, of the three `exotic'
structures in this LQC model, namely: curvature corrections, inverse triad
definitions and the `polymer' nature of the kinematic representation. We also
critically examine certain technical assumptions made by APS in their analysis
of WDW semiclassical states and point out some problems stemming from the
infrared behaviour of their wave functionsComment: 26 pages, no figure
Kinematic quantities of finite elastic and plastic deformation
Kinematic quantities for finite elastic and plastic deformations are defined
via an approach that does not rely on auxiliary elements like reference frame
and reference configuration, and that gives account of the inertial-noninertial
aspects explicitly. These features are achieved by working on Galilean
spacetime directly. The quantity expressing elastic deformations is introduced
according to its expected role: to measure how different the current metric is
from the relaxed/stressless metric. Further, the plastic kinematic quantity is
the change rate of the stressless metric. The properties of both are analyzed,
and their relationship to frequently used elastic and plastic kinematic
quantities is discussed. One important result is that no objective elastic or
plastic quantities can be defined from deformation gradient.Comment: v5: minor changes, one section moved to an Appendix, 26 pages, 2
figure
- …