Yang-Mills Theory in the Multisymplectic Framework

@misc{villablanco2026yangmills,
  title = {{Yang-Mills Theory in the Multisymplectic Framework}},
  author = {David Villa-Blanco},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14418},
  eprint = {2610.14418},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14418},
}

TY  - UNPB
TI  - Yang-Mills Theory in the Multisymplectic Framework
AU  - David Villa-Blanco
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14418
UR  - https://arxiv.org/abs/2610.14418
AB  - This Master's thesis develops and applies the multisymplectic field-theory framework to (pure) Yang-Mills theory. Building from the geometric foundations of jet bundles and the Poincaré-Cartan forms, the work constructs the Lagrangian multisymplectic formalism for first-order field theories, recovering the usual Euler-Lagrange field equations and extending the Poisson brackets of symplectic mechanics to a full graded Lie algebra. It then establishes the Legendre correspondence with the multisymplectic Hamiltonian formalism (in which Hamilton equations are retrieved) including the case of singular Lagrangians (where a constraint algorithm is reproduced). Breaking Lorentz covariance via a Cauchy surface slicing, the thesis then relates the covariant multisymplectic picture to an instantaneous presymplectic (infinite-dimensional) formulation in which the instantaneous De Donder equations and presymplectic brackets are obtained in a compatible way. A comprehensive treatment of symmetries then leads to multisymplectic and instantaneous momentum maps generalizations and to several versions of Noether's theorems. Specializing the formalism to principal-bundle gauge theory, the thesis identifies the multisymplectic configuration space with the bundle of connections, gauge symmetries with symmetries in the multisymplectic language and builds the Yang-Mills Lagrangian. Lastly, among many computations, the standard tensorial Yang-Mills equations and the Bianchi identity in local trivializations are retrieved, Yang-Mills conserved currents and charges are obtained and the graded algebra is derived for a special class of Hamiltonian forms.
ER  -