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Comment on higher derivative Lagrangians in relativistic theory

Mathieu Beau
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We discuss the consequences of higher derivative Lagrangians of the form $\alpha_1 A_{\mu}(x)\dot{x}^\mu$, $\alpha_2 G_{\mu}(x)\ddot{x}^\mu$, $\alpha_3 B_{\mu}(x)\dddot{x}^\mu$, $\alpha_4 K_{\mu}(x)\ddddot{x}^\mu$, $\cdots$, $U_{(n)\mu}(x)x^{(n)\mu}$ 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 $U_{(n),\mu}(x),\ n\geq1$ with the higher currents $j^{(n)\mu}=\rho(x)x^{(n)\mu}$, where $\rho(x)$ is the spatial density of mass or of electric charge. In addition, we discuss the analogy of the field $G_\mu(x)$ 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.
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Dates and versions

hal-00825545 , version 1 (24-05-2013)
hal-00825545 , version 2 (27-05-2013)
hal-00825545 , version 3 (16-08-2013)



Mathieu Beau. Comment on higher derivative Lagrangians in relativistic theory. 2013. ⟨hal-00825545v3⟩
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