https://doi.org/10.1140/epjp/s13360-024-05782-z
Regular Article
Vector field dynamics: field equations and energy tensor
1
Departamento de Estadística, Matemática e Informática and Centre of Operations Research (CIO), Universidad Miguel Hernández, 03202, Elx, Spain
2
Instituto de Matemática Multidisciplinar and Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022, Valencia, Spain
3
Departament d’Astronomia i Astrofísica, Universitat de València, 46100, Burjassot, Spain
4
Observatori Astronòmic, Universitat de València, 46980, Paterna, Spain
Received:
13
June
2024
Accepted:
24
October
2024
Published online:
21
November
2024
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the general Euler–Lagrange equations for the field are derived and the existence of a conserved current is achieved. The field equations are also analysed from an eikonal-like point of view. The Hilbert energy-momentum tensor of the field is also derived and the influence of each one of the irreducible pieces appearing in the Lagrangian is studied. Particular values of the free parameters allow to retrieve known results.
Alicia Herrero and Juan Antonio Morales-Lladosa have contributed equally to this work.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
