Let 𝒫n be the trivial principal bundle with structural group G and base space 𝒫n−1, 𝒫1 being the usual fiber bundle of gauge theories. In order to give a geometrical interpretation to the Faddeev–Popov fields, as well as to the Becchi, Rouet, and Stora transformations, we need to use the fiber bundle 𝒫3. The gauge fields and the Faddeev–Popov ghost and antighost fields appear as part of certain 1‐forms defined on the base space 𝒫2. The anticommuting character of the ghost and antighost fields is essentially due to their identification with 1‐forms. The Becchi, Rouet, and Stora transformations are identified with generalized infinitesimal gauge transformations on 𝒫3 of parameters related to the ghost fields. We obtain a further invariance of the action given by a similar generalized infinitesimal gauge transformation on 𝒫3 related to the antighost fields.
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August 1981
Research Article|
August 01 1981
Geometrical structure of Faddeev–Popov fields and invariance properties of gauge theories
M. Quirós;
M. Quirós
Instituto de Estructura de la Materia Conseio Superior de Investigaciones Científicas, Serrano 119, Madrid 6, Spain and Departmento de Física, Universidad de Alcalá de Henares, Madrid, Spain
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F. J. de Urries;
F. J. de Urries
Instituto de Estructura de la Materia Conseio Superior de Investigaciones Científicas, Serrano 119, Madrid 6, Spain and Departmento de Física, Universidad de Alcalá de Henares, Madrid, Spain
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J. Hoyos;
J. Hoyos
Departmento de Matemáticas, Universidad de Alcalá de Henares, Madrid, Spain
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M. L. Mazón;
M. L. Mazón
Departmento de Matemáticas, Universidad de Alcalá de Henares, Madrid, Spain
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E. Rodriguez
E. Rodriguez
Departmento de Matemáticas, Universidad de Alcalá de Henares, Madrid, Spain
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J. Math. Phys. 22, 1767–1774 (1981)
Citation
M. Quirós, F. J. de Urries, J. Hoyos, M. L. Mazón, E. Rodriguez; Geometrical structure of Faddeev–Popov fields and invariance properties of gauge theories. J. Math. Phys. 1 August 1981; 22 (8): 1767–1774. https://doi.org/10.1063/1.525123
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