Derivation of Poincare Invariance from general quantum field theory

TL;DR

This paper attempts to derive Poincare invariance from a general quantum field theory without assuming it, revealing connections to higher dimensions and emergent spacetime symmetries at low energies.

Contribution

It introduces a framework starting from a general quantum field theory to derive Poincare invariance, linking degrees of freedom to higher dimensions and emergent spacetime symmetries.

Findings

Translational invariance can be derived assuming background parameters as gravitational fields.

Quantum electrodynamics emerges in 3+1 dimensions from the model.

Photon and Weyl fermions have separate metric tensors, indicating incomplete unification.

Abstract

Starting from a very general quantum field theory we seek to derive Poincare invariance in the limit of low energy excitations. We do not, of course, assume these symmetries at the outset, but rather only a very general second quantised model. Many of the degrees of freedom on which the fields depend turn out to correspond to a higher dimension. We are not yet perfectly successful. In particular, for the derivation of translational invariance, we need to assume that some background parameters, which a priori vary in space, can be interpreted as gravitational fields in a future extension of our model. Assuming translational invariance arises in this way, we essentially obtain quantum electrodynamics in just 3 + 1 dimensions from our model. The only remaining flaw in the model is that the photon and the various Weyl fermions turn out to have their own separate metric tensors.