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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2310.01492 |
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| _version_ | 1866909145806929920 |
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| author | Bucciotti, Bruno Strocchi, Franco |
| author_facet | Bucciotti, Bruno Strocchi, Franco |
| contents | The quantization of Yang-Mills field theories requires the introduction of a gauge fixing which leads to a violation of the Local Gauss Law described by the so-called Gauss operator. We discuss the local quantizations of Yang-Mills theories in terms of the possible Gauss operators, which are argued to have a more physical meaning than the gauge fixings. We focus the attention on the local quantizations which leave the global gauge group and a subgroup of local gauge transformations unbroken, as the Feynman quantization of quantum Electrodynamics, and show that in the non-abelian case such properties cannot be realized together with Lorentz covariance; thus, quite generally, one cannot have the structural properties of the Feynman quantization of Quantum Electrodynamics. By relaxing the condition of Lorentz covariance, we obtain a classification of Gauss operators, which satisfy gauge covariant conservation laws and generate non-trivial residual subgroups of local gauge transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01492 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on Gauss operators and quantizations of Yang-Mills theories Bucciotti, Bruno Strocchi, Franco High Energy Physics - Theory The quantization of Yang-Mills field theories requires the introduction of a gauge fixing which leads to a violation of the Local Gauss Law described by the so-called Gauss operator. We discuss the local quantizations of Yang-Mills theories in terms of the possible Gauss operators, which are argued to have a more physical meaning than the gauge fixings. We focus the attention on the local quantizations which leave the global gauge group and a subgroup of local gauge transformations unbroken, as the Feynman quantization of quantum Electrodynamics, and show that in the non-abelian case such properties cannot be realized together with Lorentz covariance; thus, quite generally, one cannot have the structural properties of the Feynman quantization of Quantum Electrodynamics. By relaxing the condition of Lorentz covariance, we obtain a classification of Gauss operators, which satisfy gauge covariant conservation laws and generate non-trivial residual subgroups of local gauge transformations. |
| title | A note on Gauss operators and quantizations of Yang-Mills theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2310.01492 |