Generalized Yang-Mills Theory under Rotor Mechanism

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 $T_{\mu }^a\to {\square }^n{T}_{\mu }^a$. 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.

17 pages

References in corpus (5)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Lee-Wick Standard Model
• Third order equations of motion and the Ostrogradsky instability
• Classical and quantum stability of higher-derivative dynamics
• On the instability of classical dynamics in theories with higher derivatives