Related papers: A Local Gauge-Covariant Formulation of Classical D…
We introduce cosurfaces with values in the group \(\PC_n(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coefficients and contravariant on lower triangular coefficients,…
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical…
Quantum dynamics of coherent states is studied within quantum field theory using two complementary methods: by organizing the evolution as a Taylor series in elapsed time and by perturbative expansion in coupling within the…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
The global time is defined in covariant form under the condition of a constant mean curvature slicing of spacetime. The background static metric is taken in the tangent space. The global intrinsic time is identified with the logarithmic…
For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor…
We propose a first-order geometric Lagrangian for four-dimensional conformal gravity within the Cartan formulation, which yields, dynamically, the standard constraints on the fields, expected for conformal gravity. Upon imposing the…
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…
Using our recent proposal for defining gauge invariant averages we give a general-covariant formulation of the so-called cosmological "backreaction". Our effective covariant equations allow us to describe in explicitly gauge invariant form…
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the…
In it's usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
It is argued that the formal rules of correspondence between local observation procedures and observables do not exhaust the entire physical content of generally covariant quantum field theory. This result is obtained by expressing the…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
Scaling symmetries have previously been examined for classical field theories described by singular Lagrangians; in this article, we apply these results to the first-order formulation of General Relativity. It is shown that the dynamical…
We discuss the covariant formulation of the dynamics of particles with abelian and non-abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…