Generalized Yang-Mills Theory under Rotor Mechanism

TL;DR

This paper extends Yang-Mills theory to include higher-order derivatives using the rotor mechanism, maintaining gauge invariance and analyzing stability, thus providing a broader framework for non-abelian gauge fields.

Contribution

It generalizes Yang-Mills theory with higher derivatives via the rotor mechanism and explores its equations of motion, symmetries, and stability properties.

Findings

Rotor mechanism applies to non-abelian case under Lorentz gauge.

Generalized theory reduces to original Yang-Mills when derivative order is zero.

Identified potential dynamic instabilities through Ostrogradsky analysis.

Abstract

This paper follows the previous work on generalized abelian gauge field theory of higher-order derivatives under rotor model and extends the study to the most generalized non-abelian case. We find that the rotor mechanism from the abelian case applies nicely to the non-abelian case under the Lorentz gauge condition. Under the rotor mechanism, the gauge field transforms as $T_{\mu}^a \rightarrow \Box^n T_{\mu}^a$. When the order of field derivative is $n=0$, this restores back to the original Yang-Mills action. Our work gives an extensive generalization of the Yang-Mills theory with higher-order field derivatives. We also compute the equation of motion and Noether's current of the generalized non-abelian gauge field theory. Finally, we study the dynamic instability issue of the theory by the Ostrogradsky construction and the analysis of the 00-component of the energy-momentum tensor.