Narciso Román Roy

On the k-symplectic, k-cosymplectic and multisymplectic formalisms of classical field theories

The objective of this work is twofold: First, we analyze the relation between the

Variational principles and symmetries on fibered multisymplectic manifolds

k

SOPDEs and nonlinear connections

-cosymplectic and the

Mathematical foundations of geometric quantization

k

A new multisymplectic unified formalism for second order classical field theories

-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between

Hamilton-Jacobi theory and the evolution operator

k

Multivector Fields and Connections. Applications to field theories

-symplectic field theories and the so-called autonomous

Origen y desarrollo histórico del cálculo infinitesimal

k

Lie-algebroid formulation of k-cosymplectic classical field theories

-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between

Algunas conclusiones del Primer Encuentro "Mujeres y Matemáticas" de la Real Sociedad Matemática Española

k