Groupoid Representation of Lorentz Transformations Including Superluminal Observers

Abstract:We construct a Minkowski-pointed Poincare groupoid that extends the geometric description of Lorentz transformations to frames superluminal relative to a distinguished rest frame. Real four-dimensional superluminal boost matrices factorize into ordinary Lorentz boosts and finite infinite-speed limits. For each spatial direction, the two oriented limits define arrows between the Minkowski metric object and a directional metric object; their composition yields an involutive isotropy loop generating a direction-dependent extension of the Poincare group. These arrows induce *-isomorphisms of Poincare observable algebras, transporting generators and their tensor products. Since all metric objects share a common affine spacetime and dual momentum space, transported spectral data can be classified relative to the distinguished Minkowski metric. This Minkowski-pointed classification recovers ordinary massive and massless Wigner sectors and assigns spacelike orbits, with SO(2,1) little groups, to massive momentum representatives transported to directional objects. It thus provides a geometric interpretation of tachyonic Wigner wavefunction classes without postulating intrinsically tachyonic states. As a kinematic application, we examine polarized cobalt-60 beta decay. Under an explicit source-arrow correspondence, reversal of nuclear polarization exchanges oriented arrows and reverses the preferred momentum direction, consistently with the observed reversal of the Wu counting asymmetry. The measured angular law is compatible with this correspondence; a derivation of decay amplitudes and asymmetry coefficients remains open.

arXiv:2510.25385 [hep-th]

(or arXiv:2510.25385v4 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2510.25385 Focus to learn more arXiv-issued DOI via DataCite

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