Related papers: Lecture Notes on Mathematical Methods of Classical…
We consider classical gauge theory with spontaneous symmetry breaking on a principal bundle $P\to X$ whose structure group $G$ is reducible to a closed subgroup $H$, and sections of the quotient bundle $P/H\to X$ are treated as classical…
We present an alternative field theoretical approach to the definition of conserved quantities, based directly on the field equations content of a Lagrangian theory (in the standard framework of the Calculus of Variations in jet bundles).…
This note gives an introduction to Lagrangian field theories in the presence of boundaries. After an overview of the classical aspects, the cohomological formalisms to resolve singularities in the bulk and in the boundary theories (the BV…
In this talk the description of gauge theories associated with internal symmetries is extended to the case in which the symmetry group is the space-time translation group (recovering Einstein's theory) using the standard jet-bundle…
Some years ago, a new powerful technique, known as the Classical Effective Field Theory, was proposed to describe classical phenomena in gravitational systems. Here we show how this approach can be useful to investigate theoretically…
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of $k$-cosymplectic geometry. We discuss the relation between Lagrangian and Hamiltonian…
We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and…
In this paper using the Clifford bundle formalism a Lagrangian theory of the Yang-Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski spacetime is presented. It is shown how two simple…
A new geometric framework is developed to describe non-conservative classical field theories, which is based on multisymplectic and contact geometries. Assuming certain additional conditions and using the forms that define this multicontact…
In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves as well as stationary fields like…
We briefly review the universal supersymmetry present in classical hamiltonian systems and show its applications to field theories.
Motivated by the study of physical models associated with General Relativity, we review some finite-dimensional, geometric and covariant formulations that allow us to characterize in a simple manner the symmetries for classical field theory…
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions…
In the jet bundle description of Field Theories (multisymplectic models, in particular), there are several choices for the multimomentum bundle where the covariant Hamiltonian formalism takes place. As a consequence, several proposals for…
A number of recent works in E-print arXiv have addressed the foundation of gauge gravitation theory again. As is well known, differential geometry of fibre bundles provides the adequate mathematical formulation of classical field theory,…
In this paper we extend the geometric formalism of Hamilton-Jacobi theory for Mechanics to the case of classical field theories in the k-symplectic framework.
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined via the (Hamiltonian)…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
We present a classification of hamiltonian vector fields on multisymplectic and polysymplectic fiber bundles closely analogous to the one known for the corresponding dual jet bundles that appear in the multisymplectic and polysymplectic…