Geometric Gauge Freedom in Multisymplectic Field Theories

Abstract

We use the kernel of a premultisymplecic form to classify its solutions, inspired by the work of M. Gotay and J. Nester. In the case of variational premultisymplectic forms, there is an equivalence relation which classify the solutions in general distributions called expanded solutions. We also present an equivalence relation for sections and a reduction procedure for the system. We apply this results to mechanics, electromagnetism and Metric-Affine gravity, and compare them with other notions of gauge freedom.