Representations of Spacetime as Unitary Operation Classes or Against the Monoculture of Particle Fields

TL;DR

This paper models spacetime using classes of unitary operations, revealing a structure that incorporates both particle and nonparticle contributions, challenging the particle-centric view of quantum fields.

Contribution

It introduces a novel representation of spacetime as classes of unitary operations, linking geometric invariants to particle mass and interaction ranges, and highlights the role of nonparticle contributions.

Findings

Spacetime modeled as classes of (2) operations within (\u00a7^2).

Residual representations characterized by two real invariants, one for mass, one for interaction range.

Fields include nonparticle contributions in their propagators.

Abstract

Spacetime is modelled as a homogeneous manifold given by the classes of unitary $\U(2)$ operations in the general complex operations $\GL(\C^2)$. The residual representations of this noncompact symmetric space of rank two are characterized by two continuous real invariants, one invariant interpreted as a particle mass for a positive unitary subgroup and the second one for an indefinite unitary subgroup related to nonparticle interpretable interaction ranges. Fields represent nonlinear spacetime $\GL(\C^2)/\U(2)$ by their quantization and include necessarily nonparticle contributions in the timelike part of their flat space Feynman propagator.