The second order Hamiltonian space of Electrodynamics

Abstract

One studies the Hamiltonian space of second order H⁽²⁾ⁿ = (M, H_{(x, y, p)}) endowed with the fundamental function H = 1/mc g^ij (x, y)p_ip_j− 2e/m p_iAⁱ (x, y)+ e²/mc² AⁱA^j g_ijwhere g_ij(x, y) is the fundamental tensor of a Finsler space Fⁿ = (M, F(x, y)), Aⁱ(x, y) are the electromagnetic potentials on the tangent bundle TM and m, c, e are known physical constants. One determines the Hamilton-Jacobi equations, the energy and the law of conservation of energy, as well as the Lorentz nonlinear connection of the space H⁽²⁾ⁿ.