426(6): Hamilton Jacobi Equation for Special Relativity and Rigorous Self Consistency

This note defines the hamiltonian as Eq. (1), as in the Sommerfeld equation, and shows that the Hamilton and Lagrange methods give the same equations of motion for special relativity. These are written in the inertial frame and in plane polar coordinates. So the orbital precession becomes the same in both formalisms using this new method. From the special relativistic hamiltonian (14) the Hamilton Jacobi equations (19) and (20) are derived. They can be solved to give the actions for translational and rotational motions by integrating Eqs. (19) and (20). The quantized action is the angular momentum h bar, so the Hamilton Jacobi equation is a route to quantization. The next and final step is to develop the Hamilton Jacobi equations for m theory.


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