Quantum Isometrodynamics

TL;DR

This paper develops a quantum field theory called Quantum Isometrodynamics, demonstrating its renormalizability, gauge invariance, and asymptotic freedom properties, and introduces new quantum numbers related to internal degrees of freedom.

Contribution

It generalizes classical Isometrodynamics to a quantum framework, derives Feynman rules, and proves renormalizability and asymptotic freedom for the theory.

Findings

QID is renormalizable by power counting.

Pure QID is asymptotically free for all inner space dimensions.

QID coupled to the Standard Model is not asymptotically free for D ≤ 7.

Abstract

Classical Isometrodynamics is quantized in the Euclidean plus axial gauge. The quantization is then generalized to a broad class of gauges and the generating functional for the Green functions of Quantum Isometrodynamics (QID) is derived. Feynman rules in covariant Euclidean gauges are determined and QID is shown to be renormalizable by power counting. Asymptotic states are discussed and new quantum numbers related to the "inner" degrees of freedom introduced. The one-loop effective action in a Euclidean background gauge is formally calculated and shown to be finite and gauge-invariant after renormalization and a consistent definition of the arising "inner" space momentum integrals. Pure QID is shown to be asymptotically free for all dimensions of "inner" space $D$ whereas QID coupled to the Standard Model fields is not asymptotically free for D <= 7. Finally nilpotent BRST transformations for Isometrodynamics are derived along with the BRST symmetry of the theory and a scetch of the general proof of renormalizability for QID is given.