Related papers: An Elementary Canonical Classical and Quantum Dyna…
We present a new reformulation of the canonical quantum geometrodynamics, which allows to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the…
Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…
This chapter focuses on the status of the implementation of the dynamics in the canonical version of Loop Quantum Gravity (LQG). Concretely this means to provide a mathematical meaning of the quantum Einstein equations, sometimes called…
The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive…
We discuss in this Chapter a series of theoretical developments which motivate the introduction of a quantum evolution equation for which the eikonal approximation results in the geodesics of a four dimensional manifold. This geodesic…
A key tenet of general relativity is the dynamical nature of space-time, ideally represented as an initial value problem. Here we explore the variational formulation of classical Einstein-Hilbert gravity as initial value problem by…
The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…
A generalized canonical form of multi-time dynamical theories is proposed. This form is a starting point for a modified canonical quantization procedure of theories based on a quantum version of the action principle. As an example, the…
Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…
The effort to discover a quantum theory of gravity is motivated by the need to reconcile the incompatibility between quantum theory and general relativity. Here, we present an alternative approach by constructing a consistent theory of…
This work reveals a fundamental link between general covariance and Birkhoff's theorem. We extend Birkhoff's theorem from general relativity to a broad class of generally covariant gravity theories formulated in the Hamiltonian framework.…
We present a generalized Newtonian description of particle dynamics valid for any spherically symmetric, static black hole spacetime. This approach is derived from the geodesic motion of test particles in the low-energy limit. It reproduces…
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…
Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…
We explore the features of gravity in its quantum regime in a mathematically rigorous way by carrying out the classical and quantum formulations of some two-Killing symmetry reductions of general relativity which admit an exact…
In canonical gravity, covariance is implemented by brackets of hypersurface-deformation generators forming a Lie algebroid. Lie algebroid morphisms therefore allow one to relate different versions of the brackets that correspond to the same…
't Hooft has recently developed a discretisation of (2+1) gravity which has a multiple-valued Hamiltonian and which therefore admits quantum time evolution only in discrete steps. In this paper, we describe several models in the continuum…
We propose a field theory for the local metric in Stueckelberg--Horwitz--Piron (SHP) general relativity, a framework in which the evolution of classical four-dimensional (4D) worldlines $x^\mu \left( \tau \right)$ ($\mu = 0,1,2,3 $) is…
In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…