Cauchy data space and multisymplectic formulation of conformal classical field theories

Abstract

In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multi-symplectic setting comes from its suitable description of field theories, and the conformal character has been added to account for field theories that are scale invariant, flat spaces, and because some conformal fields can be exactly solved or classified. In particular, we will solve the example of a conformal scalar field using the geometric Hamilton-Jacobi theory that is explicitly proposed for conformal fields on a multisymplectic manifold. To complete the geometric approach to study field theories, we pro-pose the Hamilton-Jacobi theory for conformal fields in a Cauchy data space, in which space and time are split separately and the dynamics is depicted in an infinite-dimensional manifold. (c) 2021 Elsevier Inc. All rights reserved.