Constructing p, n-forms from p-forms via the Hodge star operator and the exterior derivative

In this paper, we aim to explore the properties and applications on the operators consisting of the Hodge star operator together with the exterior derivative, whose action on an arbitrary p-form field in n-dimensional spacetimes makes its form degree remain invariant. Such operations are able to gen...

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Bibliographic Details
Published in:Communications in theoretical physics 2020-06, Vol.72 (6), p.65402
Main Author: Peng, Jun-Jin
Format: Article
Language:English
Subjects:
form
Hodge star
Lagrangian for
Laplace-Beltrami operator
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Summary:In this paper, we aim to explore the properties and applications on the operators consisting of the Hodge star operator together with the exterior derivative, whose action on an arbitrary p-form field in n-dimensional spacetimes makes its form degree remain invariant. Such operations are able to generate a variety of p-forms with the even-order derivatives of the p-form. To do this, we first investigate the properties of the operators, such as the Laplace-de Rham operator, the codifferential and their combinations, as well as the applications of the operators in the construction of conserved currents. On the basis of two general p-forms, then we construct a general n-form with higher-order derivatives. Finally, we propose that such an n-form could be applied to define a generalized Lagrangian with respect to a p-form field according to the fact that it includes the ordinary Lagrangians for the p-form and scalar fields as special cases.
ISSN:0253-6102
1572-9494
DOI:10.1088/1572-9494/ab8a14