Related papers: Space-time Averages of Classical Physical Fields
We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
Teleparallel gravity, an empirically equivalent counterpart to General Relativity, represents the influence of gravity using torsional forces. It raises questions about theory interpretation and underdetermination. To better understand the…
We show how to provide suitable gauge invariant prescriptions for the classical spatial averages (resp. quantum expectation values) that are needed in the evaluation of classical (resp. quantum) backreaction effects. We also present…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory. The extended geometry distinguishes between the ordinary spacetime based…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
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.…
In this work, we present two alternative yet equivalent representation formulae for Whitney forms that are valid for any choice of coordinates, and generalizes the original characterization of Whitney forms in Whitney (1957) that requires…
Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has…
A theory in which points, lines, areas and volumes are on on the same footing is investigated. All those geometric objects form a 16-dimensional manifold, called C-space, which generalizes spacetime. In such higher dimensional space…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
We give an introductory overview of the classical Poincar\'e gauge theory of gravity formulated on the spacetime manifold that carries the Riemann-Cartan geometry with nontrivial curvature and torsion. After discussing the basic…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…
We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
We present a formalism for spatial averaging in cosmology applicable to general spacetimes and coordinates, and allowing the easy incorporation of a wide variety of matter sources. We apply this formalism to a…
In the framework of Galilei classical mechanics (i.e., general relativistic classical mechanics on a spacetime with absolute time) developed by Jadczyk and Modugno, we analyse systematically the relations between symmetries of the geometric…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…