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 s...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.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.11865006 and 11505036partially supported by the Technology Department of Guizhou province Fund under Grant Nos.[2018]5769 and[2016]1104。
文摘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.
