Dynamical Similarity in Multisymplectic Field Theory

Abstract

Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant degrees of freedom may physically be identified with empirically-inaccessible measures of global scale. In this article, we present a mathematical framework which extends the symmetry reduction procedure to theories of classical fields, in both the Lagrangian and Hamiltonian settings. In order to maintain Lorentz covariance, while simultaneously working with a finite-dimensional phase space, we employ the De Donder-Weyl formalism, for which the natural description is formulated in terms of the fibered manifolds of multisymplectic geometry. We subsequently analyse a number of simple examples, and provide a discussion of the broader implications of our construction.