de Sitter relativity in static charts

Abstract

The relative geodesic motion in static (and spherically symmetric) local charts on the (1 + 3)-dimensional de Sitter spacetimes is studied in terms of conserved quantities. The Lorentzian isometries are derived, relating the coordinates of the local chart of a fixed observer with the coordinates of a mobile chart considered as the rest frame of a massive particle freely moving on a timelike geodesic. The time dilation and Lorentz contraction are discussed pointing out some notable features of the de Sitter relativity in static charts.

Propagators of the Dirac fermions on spatially flat FLRW space–times

“…However, these propagators, depending explicitely on the Heaviside step functions, cannot be used in calculating Feynman diagrams without an integral rep. which should encapsulate the effect of these functions. This is why we proposed recently a new type of integral rep. which takes over the effect of the step functions but is different from the Fourier integrals used in special relativity [13]. Thus we completed the theory of the free Dirac fermions on the de Sitter expanding universe [14,15,16] with the integral rep. of the Feynman propagators we need for calculating physical effects in our de Sitter quantum electrodynamics (QED) in Coulomb gauge [17] using perturbations.…”

Collective classical motion on hyperbolic spacetimes of any dimensions

“…In our investigations we observed that on dS and AdS spacetimes there are special static charts [8,9] with Cartesian coordinates in which the geodesic equations can be expressed simply, in terms of conserved quantities, without using explicitely initial conditions [4,5,7]. These results can be generalized easily to any dimensions by using the same type of static charts.…”

“…Finally we note that here we respected up to signs our previous definitions given in the cases of d = 3 for the dS [3,4] and AdS [6,7] manifolds. Therefore, we find similar flat limits (for ω → 0) that read…”

“…The ( Note that the hyperbolic spacetimes have the coset structure M ± ∼ G ± /G 0 [17] we have exploited for building the dS and AdS relativity [7,3,4]. For the group G and its subgroups we use the canonical parametrization…”

“…The (1 + 3)-dimensional hyperbolic manifolds, the de Sitter (dS) and antide Sitter (AdS) spacetimes, are interesting because of their isometries which generate a large collection of conserved quantities which may be used for studying classical systems on these manifolds [1,2,3,4,5,6,7].…”