Generalized Yang-Mills theory under rotor mechanism

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 <math altimg="si1.svg"><msubsup><mrow><mi>T</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>a</mi></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mo>□</mo></mrow><mrow><mi>n</mi></mrow></msup><msubsup><mrow><mi>T</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>a</mi></mrow></msubsup></math>. When the order of field derivative is <math altimg="si2.svg"><mi>n</mi><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mn>0</mn></math>, 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.