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We face the well-known gyrokinetic problem, which arises in the description of the dynamics of a charged particle subject to fast gyration for the presence of a strong electromagnetic field. The customary approach to gyrokinetic theory,…
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…
We extend the theory of the gauging of classical quadratically nonlinear algebras without a central charge but with a coset structure, to the quantum level. Inserting the minimal anomalies into the classical transformation rules of the…
Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with non-renormalizable scalar models as well as quantum gravity. The basic applications of this approach lead to the common goals of any…
A new form of the dynamical equations of vacuum general relativity is proposed. This form involves the canonical Hamiltonian structure but non canonical variables. The new field variables are the electric field $E^{a}{}_{i}$ and the…
The favored classical variables that are promoted to quantum operators are divided into three sets that feature constant positive curvatures, constant zero curvatures, as well as constant negative curvatures. This list covers the spin…
A novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and…
In this PhD thesis, we introduced a new strategy to investigate the kinematical and physical predictions of self dual Loop Quantum Gravity (LQG) and by-passed the old problem of implementing quantum mechanically the so called reality…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a…
We study canonical transformations of general relativity (GR) to provide a novel matter coupling to gravity. Although the transformed theory is equivalent to GR in vacuum, the equivalence no longer holds if a matter field minimally couples…
We study gauge theories and quantum gravity in a finite interval of time $\tau $, on a compact space manifold $\Omega $. The initial, final and boundary conditions are formulated in gauge invariant and general covariant ways by means of…
We present a new approach to the covariant canonical formulation of Einstein-Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…
In a remarkable paper, T. Koslowski introduced kinematical representations for loop quantum gravity in which there is a non-degenerate spatial background metric present. He also considered their properties, and showed that Gauss and…
We work on a spacetime manifold foliated by timelike leaves. In this setting, we explore the solution of the second-class constraints arising during the canonical analysis of the Holst action with a cosmological constant. The solution is…
We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the…
We write down a quantum gravity equation which generalizes the Wheeler-DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries…
We argue that the standard canonical treatment of GR breaks manifest spacetime covariance. We present new variables which carry a reducible representation of gauge transformations and spacetime diffeomorphisms. A proposal is presented for…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…