Lorentz-invariant quantum fields in the space-time tangent bundle
type: Item
instance of: scholarly article
title: Lorentz-invariant quantum fields in the space-time tangent bundle
zbMATH Open document ID: 1028.81042
DOI: 10.1155/S0161171203109076
author: Howard E. Brandt
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/50494
review text: The author considers theory of `maximal-acceleration invariant scalar field'. Such a field \(\Phi\) is defined in the tangent space to the space-time. The coordinates of the tangent space include both usual space-time coordinates \(x^\mu\) and \(\rho_0 v^\mu\) where \(v^\mu\) are four-velocities and \(\rho_0 = c^2/a_0\) is expressed through the maximum possible proper acceleration \(a_0\). The field \(\Phi\) is an eigenvector, with the null eigenvalued, of the invariant Laplace-Beltrami operator. The bundle structure, upon which the Laplace-Beltrami operator is based, follows from the invariance of maximal proper acceleration as is defined in the preceding papers of the author. The field is demonstrated to have a physically based Planck-scale effective regularization with an effective spectral cutoff near the Planck mass. It was argued that provided the adjoint field is consistently generalized, the necessary commutators are vanishing and the field is microcausal. There are, however, Planck-scale modifications of the causal domain, but they only become significant for extremely large relative four-velocities at the separated space-time points. The geometry of the causal domain suggests that at the Planck scale, causal connectivity may occur between spacelike separated points and also at larger scales for extremely large relative four-velocities.
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 81R20
Mathematics Subject Classification ID: 83C47
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 83A05
zbMATH DE Number: 1930045
zbMATH Keywords: scalar field
zbMATH Keywords: tangent space
zbMATH Keywords: maximal acceleration
reviewed by: Michael B. Mensky
MaRDI profile type: Publication
OpenAlex ID: W1991690012
description: scientific article; zbMATH DE number 1930045