4.3 Article

Natural higher-derivatives generalization for the Klein-Gordon equation

Journal

MODERN PHYSICS LETTERS A
Volume 36, Issue 28, Pages -

Publisher

WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217732321502059

Keywords

Higher-derivatives models; generalized Klein-Gordon equation; Klein-Gordon equation

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This paper introduces a natural family of higher-order partial differential equations by generalizing the second-order Klein-Gordon equation. The associated model is characterized by a generalized action for a scalar field with higher-derivative terms, and the limit obtained from higher-order powers of the d'Alembertian operator is discussed. The general model is constructed using the exponential of the d'Alembertian differential operator, and canonical energy-momentum tensor densities and field propagators are explicitly computed for both homogeneous and non-homogeneous situations, resulting in classical solutions for all cases.
We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing higher-derivative terms. The limit obtained by considering arbitrarily higher-order powers of the d'Alembertian operator leading to a formal infinite-order partial differential equation is discussed. The general model is constructed using the exponential of the d'Alembertian differential operator. The canonical energy-momentum tensor densities and field propagators are explicitly computed. We consider both homogeneous and non-homogeneous situations. The classical solutions are obtained for all cases.

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