The Bundle of Tensor Densities and Its Covariant Derivatives
Year: 2024
Type: article
Abstract: We construct the smooth vector bundle of tensor densities of arbitrary weight in a coordinate-independent way. We prove the general existence of a globally smooth tensor density field, as well as the existence of a globally smooth metric density for a pseudo-Riemannian manifold, specifically. We study the coordinate description of a covariant derivative over densities, and define a natural extension of affine connections to densities. We provide an equivalent characterization, in the case of a pseudo-Riemannian manifold.
Source: Axioms
Authors: Joan Grandes Umbert, Tom Mestdag
Institution: University of Antwerp
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
OpenAlex ID: W4402859658