Comment on the higher derivative Lagrangians in relativistic theory

Beau, Mathieu (2013) Comment on the higher derivative Lagrangians in relativistic theory. (Preprint)

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Abstract

We discuss the consequences of higher derivative Lagrangians of the form (α_1)(A_μ)(x)ẋ^μ , (α_2)(G_μ)(x)ẍ^μ , · · · , U_((n)μ)(x)x^((n)μ) in relativistic theory. After establishing the equations of the motion of particles in these fields, we introduce the concept of the generalized induction principle assuming the coupling between the higher fields U_((n)μ)(x), n ≥ 1 with the higher currents j^(n)μ = ρ(x)x^(n)μ , where ρ(x) is the spatial density of mass or of electric charge. In addition, we discuss the analogy of the field G_μ(x) with the gravitational field and its inclusion in the general relativity framework in the last section. This letter is an invitation to reflect on a generalisation of the concept of inertia and we also discuss this problem in the last section.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 13:49
Last Modified: 12 Jul 2018 13:34
URI: http://dair.dias.ie/id/eprint/539

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