Consistent Quantization of the Yang-Mills Field: Noether's Theorem and Factor-Ordering Problems

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Abstract
The problem of obtaining a consistent quantization of the Yang-Mills field is examined by invoking the postulated Lorentz and gauge invariance of this theory. Because of the factor-ordering problems that arise from the nonlinear self-coupling of the theory, the Noether's theorem for these physical symmetries does not trivially follow from the invariance of the action. We formulate a set of necessary conditions for any consistent quantization of a nonlinear, non-Abelian gauge theory.