Related papers: A generalized Hamiltonian Constraint Operator in L…
In this work we investigate the question, under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelian analogues of the electric flux. We give the…
Loop Quantum Gravity faces challenges in constructing a well-defined Hamiltonian constraint and understanding the quantum notion of time. In this paper these issues are studied by quantizing the $U(1)^3$ model, a simplified system…
In this paper is considered a generalized quantization principle for the gravitational field in canonical quantum gravity, especially with respect to quantum geometrodynamics. This assumption can be interpreted as a transfer from the…
Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion…
It is argued that some approaches to non-perturbative quantum general relativity lack a sensible continuum limit that reproduces general relativity. The basic problem is that generic physical states lack long ranged correlations, because…
Quantum-reduced loop gravity is a model of loop quantum gravity, which - from the technical point of view - is characterized by the remarkably simple form of its basic operators. In this article we examine the operators of the…
The quantum affine $\CU_q (\hat{sl(2)}) $ symmetry is studied when $q^2$ is an even root of unity. The structure of this algebra allows a natural generalization of N=2 supersymmetry algebra. In particular it is found that the momentum…
In this thesis we consider the problem of dynamics in canonical loop quantum gravity, primarily in the context of deparametrized models, in which a scalar field is taken as a physical time variable for the dynamics of the gravitational…
The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In…
We suggest how to interpret the action of the quantum Hamiltonian constraint of general relativity in the loop representation as a skein relation on the space of knots. Therefore, by considering knot polynomials that are compatible with…
We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construction which encodes the kinematics of quantum gravity. The construction is a spectral triple over a…
We provide an angular parametrization of the special unitary group $\textrm{SU}(2^{n})$ generalizing Euler angles for $\textrm{SU}(2)$ by successively applying the KAK decomposition. We then determine constraint equations for the parametric…
A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously…
We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…
Introducing a new method, we demonstrate how the action of reduced operators can be derived without resorting to a recoupling theory and how they exactly reproduce the results obtained in the standard approach of Quantum Reduced Loop…
We present a generalization of the quantum volume operator quantifying the volume in curved three-dimensional discrete geometries. In its standard form, the quantum volume operator is constructed from tetrahedra whose faces are endowed with…
We consider the transformation of Hamilton operators under various sets of quantum operations acting simultaneously on all adjacent pairs of particles. We find mappings between Hamilton operators analogous to duality transformations as well…