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PreprintCC BY 4.0arXiv

Gauge invariant generalizations of the Proca equation and the Yang-Mills-Proca equation

  • Nikolay Marchuk
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Abstract

The Proca equations (1936) are used in quantum field theory to describe vector bosons (spin 1) with a nonzero mass. The Proca equations are not gauge invariant. In contrast to Stueckelberg's approach (1938), this article presents a gauge invariant generalization of the Proca equation by introducing an additional vector field into the Proca equation. The results are extended to the Yang-Mills-Proca equations, leading to equations with non-Abelian gauge symmetry.

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Cite

BibTeXRIS
BibTeX
@misc{marchuk2026gauge,
  title = {{Gauge invariant generalizations of the Proca equation and the Yang-Mills-Proca equation}},
  author = {Nikolay Marchuk},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2606.20828},
  eprint = {2606.20828},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.20828},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Gauge invariant generalizations of the Proca equation and the Yang-Mills-Proca equation
AU  - Nikolay Marchuk
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2606.20828
UR  - https://arxiv.org/abs/2606.20828
AB  - The Proca equations (1936) are used in quantum field theory to describe vector bosons (spin 1) with a nonzero mass. The Proca equations are not gauge invariant. In contrast to Stueckelberg's approach (1938), this article presents a gauge invariant generalization of the Proca equation by introducing an additional vector field into the Proca equation. The results are extended to the Yang-Mills-Proca equations, leading to equations with non-Abelian gauge symmetry.
ER  -