Related papers: Testing the Master Constraint Programme for Loop Q…
We investigate refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling a momentum-type constraint. The quantum constraint is implemented by a…
A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
The Hamiltonian description for a wide class of mechanical systems, having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order, is constructed. The Poisson brackets of the Hamiltonian and…
We study the deformation quantisation (Moyal quantisation) of general constrained Hamiltonian systems. It is shown how second class constraints can be turned into first class quantum constraints. This is illustrated by the O(N) non-linear…
In this work we introduce a criterion for testing general covariance in effective quantum gravity theories. It adapts the analysis of invariance under general spacetime diffeomorphisms of the Einstein-Hilbert action to the case of effective…
We analyze the issue of anomaly-free representations of the constraint algebra in Loop Quantum Gravity (LQG) in the context of a diffeomorphism-invariant gauge theory in three spacetime dimensions. We construct a Hamiltonian constraint…
The construction of effective Hamiltonians arising from Loop Quantum Gravity and incorporating Planck scale corrections to the dynamics of photons and spin 1/2 particles is summarized. The imposition of strict bounds upon some parameters of…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
The use of techniques from loop quantum gravity for cosmological models may solve some difficult problems in quantum cosmology. The solutions under a number of circumstances have been well studied. We will analyse the behaviour of solutions…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
In the context of loop quantum cosmology, we parametrise the lattice refinement by a parameter, $A$, and the matter Hamiltonian by a parameter, $\delta$. We then solve the Hamiltonian constraint for both a self-adjoint, and a…
The quantum cosmology of two-dimensional dilaton-gravity models is investigated. A class of models is mapped onto the constrained oscillator-ghost-oscillator model. A number of exact and approximate solutions to the corresponding…
Generalized Dilaton Theories in two dimensions coupled to Dirac fermions are subjected to constraint analysis. Three first class secondary constraints are found, corresponding to one local Lorentz symmetry and two diffeomorphisms. Moreover,…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements…
It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above…
The Wilson loop functionals in terms of Ashtekar's variables were the first (formal) solutions to the quantized hamiltonian constraint of canonical gravity. Here it is shown that the same functionals also solve the supergravity constraints…
Loop quantum gravity methods are applied to a symmetry-reduced model with homogeneity in two dimensions, derived from a Gowdy model [5,6]. The conditions for propagation of unidirectional plane gravitational waves at exactly the speed of…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…