Ultraviolet behavior in background independent quantum field theory

TL;DR

This paper introduces a background independent quantization of scalar fields revealing energy-dependent behaviors, a transition to fermionic characteristics at high energies, and modified dispersion relations, indicating fundamental ultraviolet changes in quantum field theory.

Contribution

It presents a novel background independent quantization method that modifies ultraviolet properties and reveals a fermionic transition at high energies.

Findings

Energy-dependent vacuum expectation values of operators

Transition to fermionic behavior at high energy

Modified dispersion relation with cubic momentum correction

Abstract

We describe a background independent quantization of the scalar field that provides an explicit realization of Fock-like states and associated operators in a polymer Hilbert space. The vacuum expectation values of the commutator and anti-commutator of the creation and annihilation operators become energy dependent, and exhibit a surprising transition to fermionic behavior at high energy. Furthermore the approach yields a modified dispersion relation with a leading correction proportional to the momentum cubed. These results suggests a fundamental change in the ultraviolet properties of quantum fields.