Lorentz-invariant quantum fields in the space-time tangent bundle

Abstract

A maximal-acceleration invariant quantum field is defined on the space-time tangent bundle with vanishing eigenvalue when acted on by the Laplace-Beltrami operator of the bundle, and the case is addressed in which the space-time is Minkowskian, and the field is Lorentz invariant. In this case, the field is shown to be automatically regularized at the Planck scale, and particle spectra are cut off at extremely high energies. The microcausality is addressed by calculating the appropriate field commutators; and it is shown that provided the adjoint field is consistently generalized, the necessary commutators are vanishing and the field is microcausal, but that there are Planck-scale modifications of the boundary of the causal domain that are significant for extremely large relative four-velocities between the separated space-time points. For vanishing relative four-velocity, the causal domain is canonical. The geometry of the causal domain indicates that near the Planck scale, causal connectivity may occur between spacelike separated points, and also at larger scales for extremely large relative four-velocities.