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

• 来源期刊: 理论物理通讯（英文版）
• 年，卷（期）: 2020,（6）
• 页码范围: 97-105
• 页数: 9页
• 语种: 英文

摘要

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.