Gauge Field Theory in terms of complex Hamilton Geometry

On the total space of a G−complex vector bundle E is defined the gauge transformations. A gauge complex invariant Lagrangian determines a special complex nonlinear connection for which the associated Chern-Lagrange and Bott complex connections are gauge invariant. The complex field equations are determined with respect to these associated gauge complex connections. By complex Legendre transformation (the L−dual process) we investigate the similar problems on the dual vector bundle E∗. The L−dual Chern-Hamilton and Bott complex connections are also gauge invariant. The complex Hamilton equations are write for the general L−dual Hamiltonian obtained as a sum of particle Hamiltonian, Yang-Mills and Hilbert-Einstein Hamiltonians. M.S.C. 2000: 53B40, 53B50.