Dear Domenico Oricchio,
I am quoting from your essay and wondering if another professional might offer their opinion about this:
"Each time variable system can be modeled using arbitrary differential equation:
...(some non-reproducible math)...
the strange result is that the volume restrictions in the phase space are ever true (Lee Hwa-chung invariants and Poincare invariant); the dynamic of the momentum is necessary to preserve the invariants, and it has arbitrary initial conditions.
I can write the classican Hamilton-Jacobi equation and the Schrodinger equation (using the quantum correspondence) for each time variable system:
...(Some non-reproducible math)...
these equations are equal! This is a wave function dynamic (if PSI is a solution then PSI^alpha is a solution: we can use wave function or probability) and this is true for each Hamiltonian linear in the momentums! Interesting...
The ideas of Hamilton, Schrodinger, De Broglie and Bohm can converge in the same theory.
It is possible demonstrate that each time variable system is Lagrangian using the Weierstrasse theorem (trajectories like extremal fields)."
James
