Derivation of Poincaré invariance from general quantum field theory

Abstract

Abstract Starting from a very general quantum field theory we seek to derive Poincaré 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.

Locations

• Annalen der Physik - View
• arXiv (Cornell University) - View - PDF