Abstract
Spacetime is modelled by binary relations—by the classes of the automorphisms \({\text{GL(}}\mathbb{C}^2 )\) of a complex two-dimensional vector space with respect to the definite unitary subgroup U(2). In extension of Feynman propagators for particle quantum fields representing only the tangent spacetime structure, global spacetime representations are given, formulated as residues using energy–momentum distributions with the invariants as singularities. The associated quantum fields are characterized by two invariant masses—for time and position—supplementing the one mass for the definite unitary particle sector with another mass for the indefinite unitary interaction sector without asymptotic particle interpretation.
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Saller, H. Residual Representations of Spacetime. International Journal of Theoretical Physics 40, 1209–1248 (2001). https://doi.org/10.1023/A:1017593920813
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DOI: https://doi.org/10.1023/A:1017593920813