Piecewise linear loop quantum gravity
نویسندگان
چکیده
We define a modification of loop quantum gravity (LQG) in which graphs are required to consist of piecewise linear edges, which we call piecewise linear LQG (plLQG). At the diffeomorphism-invariant level, we prove that plLQG is equivalent to standard LQG, as long as one chooses the class of diffeomorphisms appropriately. That is, we exhibit a unitary map between the diffeomorphism-invariant Hilbert spaces that maps physically equivalent operators into each other. In addition, using the same ideas as in standard LQG, one can define a Hamiltonian and master constraint in plLQG, and the unitary map between plLQG and LQG then provides an exact isomorphism of dynamics in the two frameworks. Furthermore, loop quantum cosmology (LQC) can be exactly embedded into plLQG. This allows a prior program of the author to embed LQC into LQG at the dynamical level to proceed. In particular, this allows a formal expression for a physically motivated embedding of LQC into LQG at the diffeomorphism-invariant level to be given. PACS numbers: 04.60.Ds, 04.60.Kz, 04.60.Pp, 02.40.Re, 02.40.Sf
منابع مشابه
Approximate Solution of Sensitivity Matrix of Required Velocity Using Piecewise Linear Gravity Assumption
In this paper, an approximate solution of sensitivity matrix of required velocity with final velocity constraint is derived using a piecewise linear gravity assumption. The total flight time is also fixed for the problem. Simulation results show the accuracy of the method. Increasing the midway points for linearization, increases the accuracy of the solution, which this, in turn, depends on the...
متن کاملAutomorphisms in Loop Quantum Gravity
We investigate a certain distributional extension of the group of spatial diffeomorphisms in Loop Quantum Gravity. This extension, which is given by the automorphisms Aut(P) of the path groupoid P, was proposed by Velhinho and is inspired by category theory. This group is much larger than the group of piecewise analytic diffeomorphisms. In particular, we will show that graphs with the same comb...
متن کاملPhysical Diffeomorphisms in Loop Quantum Gravity
We investigate the action of diffeomorphisms in the context of Hamiltonian Gravity. By considering how the diffeomorphism-invariant Hilbert space of Loop Quantum Gravity should be constructed, we formulate a physical principle by demanding, that the gauge-invariant Hilbert space is a completion of gauge(i.e. diffeomorphism-)orbits of the classical (configuration) variables, explaining which ext...
متن کاملar X iv : 0 70 9 . 34 65 v 1 [ gr - q c ] 2 1 Se p 20 07 Dynamical Quantum Geometry ( DQG Programme )
In this brief note (written as a lengthy letter), we describe the construction of a representation for the Weyl-algebra underlying Loop Quantum Geometry constructed from a diffeomorphism variant state, which corresponds to a ”condensate” of Loop Quantum Geometry, resembling a static spatial geometry. We present the kinematical GNS-representation and the gaugeand diffeomorphism invariant Hilbert...
متن کاملPresentation of quasi-linear piecewise selected models simultaneously with designing of bump-less optimal robust controller for nonlinear vibration control of composite plates
The idea of using quasi-linear piecewise models has been established on the decomposition of complicated nonlinear systems, simultaneously designing with local controllers. Since the proper performance and the final system close loop stability are vital in multi-model controllers designing, the main problem in multi-model controllers is the number of the local models and their position not payi...
متن کامل