Role of the subsidiary fields in the momentum and angular momentum in covariantly quantized QED and QCD

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Abstract
The covariant quantization of QED and QCD requires the introduction of subsidiary gauge-fixing and ghost fields and it is crucial to understand the role of these in the energy-momentum tensor, and in the momentum and angular momentum operators. These issues were discussed by E. Leader [ Phys. Rev. D 83, 096012 (2011)], and certain key results from this study, namely that the subsidiary and ghost fields do not contribute to the physical matrix elements of the canonical or Bellinfante momentum and angular momentum, were utilized in the major review of angular momentum by E. Leader and C. Lorce [ Phys. Rep., 541, 163 (2014)]. B. Damski [ Phys. Rev. D 104, 085003 (2021)] has rightly criticized as incorrect the derivation of these results for the QED case by Leader (2011) and has given explicit expressions for the contribution of the subsidiary fields to the physical matrix elements of the QED momentum and angular momentum. We show, however, that the key results of Leader (2011), mentioned above, which are utilized by Leader and Lorce (2014), are unaffected by Damski’s criticism and that his expressions for the contribution from the subsidiary fields, in fact, vanish.

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