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arXiv · 1604.02074

Order reduction, projectability and constraints of second-order field theories and higher-order mechanics

Jordi Gaset·Narciso Román-Roy
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Abstract

The projectability of Poincaré-Cartan forms in a third-order jet bundle $J^3π$ onto a lower-order jet bundle is a consequence of the degenerate character of the corresponding Lagrangian. This fact is analyzed using the constraint algorithm for the associated Euler-Lagrange equations in $J^3π$. The results are applied to study the Hilbert Lagrangian for the Einstein equations (in vacuum) from a multisymplectic point of view. Thus we show how these equations are a consequence of the application of the constraint algorithm to the geometric field equations, meanwhile the other constraints are related with the fact that this second-order theory is equivalent to a first-order theory. Furthermore, the case of higher-order mechanics is also studied as a particular situation.

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Jordi Gaset, Narciso Román-Roy. 2016-08-12. Order reduction, projectability and constraints of second-order field theories and higher-order mechanics. https://doi.org/10.1016/s0034-4877(17)30012-5

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