Related papers: Testing the Master Constraint Programme for Loop Q…
Two models with linear and nonlinear second class constraints are considered and gauged by embedding in an extended phase space. These models are the free non-relativistic particle on a hyperplane and hyper sphere in configuration space.…
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been emphasised frequently. This idea has been picked…
We consider a second degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting in its quantum…
In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint…
We perform the Hamiltonian analysis of 1+1 dimensional non-linear massive gravity studied in arXiv:1107.3820. We find the constraint structure of given theory and perform the counting of the physical degrees of freedom.
We shall here perform the canonical analysis of field equations of ABI model in order to determine constraint equations. We shall show that one can use algebraic constraints in the covariant framework to fix $k^i$ as a function of the frame…
We show that for a system containing a set of general second class constraints which are linear in the phase space variables, the Abelian conversion can be obtained in a closed form and that the first class constraints generate a…
This work demonstrates that a complete description of the interaction of matter and all forces, gravitational and non-gravitational, can in fact be realized within a quantum affine algebraic framework. Using the affine group formalism, we…
We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and…
We reconsider the Rovelli-Smolin model of gravity coupled to the Klein-Gordon time field with an eye towards capturing the degrees of freedom of the scalar field lost in the framework in which time is deparametrized by the scalar field.…
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…
In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a…
A covariant quantization method for physical systems with reducible constraints is presented.
The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first- and second-class constraints from the point of view of…
In this paper we demonstrate closure of the quantum algebra of Hamiltonian constraints in a theory directly related to a certain sector of general relativity reduced to diagonal variables.
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
To appear in proceedings of II Workshop on ``Constraints Theory and Quantisation Methods''Montepulciano (Siena) 1993} General discussion of the constraints of 2+1 gravity, with emphasis on two approaches, namely the second order and first…
We propose a necessary and sufficient test to determine whether a solution for a general quadratic program with two quadratic constraints (QC2QP) can be computed from that of a specific convex semidefinite relaxation, in which case we say…
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the…