The Lagrangian-Hamiltonian formalism in gauge complex field theories
2006jbo | Munteanu Gh.

An introduction in the study of gauge field theory in terms of complex Finsler geometry on the total space of a $G$-complex vector bundle $E$ was made by us in \cite{Mu2}. Here we briefly recal the obtained results and similar notions are investigated on the dual bundle $E^{*}$ by complex Legendre transformation (the $\mathcal{L}$-dual process).
The complex field equations are determined with respect to a gauge complex vertical connections. The complex Hamilton equations are write for the general $\mathcal{L}$-dual Hamiltonian obtained as a sum of particle Hamiltonian, Yang-Mills and Hilbert-Einstein Hamiltonians.

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