Residual Representations of Spacetime

TL;DR

This paper models spacetime using automorphisms of complex vector spaces and introduces global spacetime representations as residues of energy-momentum distributions, highlighting invariant masses for different sectors.

Contribution

It extends Feynman propagators to global spacetime representations using residues, incorporating dual invariant masses for particle and interaction sectors.

Findings

Global spacetime representations formulated as residues.

Introduction of two invariant masses for different sectors.

Extension of Feynman propagators to a broader spacetime model.

Abstract

Spacetime is modelled by binary relations - by the classes of the automorphisms $\GL(\C^2)$ of a complex 2-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 associatated 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.