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arXiv · 2402.07847

Canonical Lifts in Multisymplectic De Donder-Weyl Hamiltonian Field Theories

Arnoldo Guerra IV·Narciso Román-Roy
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Abstract

In this paper, we define canonical lifts of vector fields to the multisymplectic multimomentum bundles of De Donder-Weyl Hamiltonian first-order field theories and to the appropriate premultisymplectic embedded constraint submanifolds on which singular field theories are studied. These new canonical lifts are used to study the so-called natural Noether symmetries present in both regular and singular Hamiltonian field theories along with their associated conserved quantities obtained from Noether's theorem. The Klein-Gordon field, the Polyakov bosonic string, and Einstein-Cartan gravity in 3 + 1 dimensions are analyzed in depth as applications of these concepts; as a peripheral result obtained in the analysis of the bosonic string, we provide a new geometrical interpretation of the well-known Virasoro constraint.

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Arnoldo Guerra IV, Narciso Román-Roy. 2024-02-12. Canonical Lifts in Multisymplectic De Donder-Weyl Hamiltonian Field Theories. https://arxiv.org/abs/2402.07847

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