Lorentz-invariant quantum fields in the space-time tangent bundle
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.
scientific article; zbMATH DE number 1930045