Diff invariant Poincare transformations as deformation of Poincare algebra

TL;DR

This paper explores how $Diff^4$ invariant Poincare transformations can be viewed as a Lorentz invariant deformation of the Poincare algebra, potentially impacting the understanding of time, irreversibility, and quantum S-matrix properties.

Contribution

It introduces a novel interpretation of $Diff^4$ invariant Poincare transformations as a specific deformation of the Poincare algebra with energy functions.

Findings

Identifies $Diff^4$ invariant transformations as a Lorentz invariant deformation.

Shows the 'new' energy as a function of 'old' energy within this deformation.

Connects the deformation to concepts of subjective time and irreversibility.

Abstract

The concept of $Diff^4$ invariant Poincare transformations is a cornerstone of T(opological) G(eometro)D(ynamics). This concept makes it possible to understand the concept of subjective time and irreversibelity as well as nontriviality of S-matrix at quantum level. In this paper the possibility of identifying $Diff^4$ invariant Poincare transformations as the recently discovered Lorentz invariant deformation of Poincare algebra with the basic property that 'new' energy is some function of 'old' energy, is considered.