10.5281/zenodo.1194698
Ruggeri Francesco R
A 2X2 Matrix Formalism Is Contained In The Relativistic Energy Momentum Equation
Zenodo
2018
2018-03-09
Preprint
https://zenodo.org/record/1194698
10.5281/zenodo.1194697
version 1
Creative Commons Attribution 4.0
Open Access
<p>In [2], it was argued that one could establish a 2x2 matrix eigenvalue equation from Einstein´s 1905 energy momentum equation p2 + m2 = E2 (1) by assuming +E and -E and making a 2x2 matrix. The purpose of this note is to show that no such assumption is necessary. The 2x2 matrix approach can be shown to follow naturally from (1). (Note: In the Dirac derivation, an argument of linearization was made in order to obtain the Dirac equation from the Klein Gordon equation.) We also propose a different argument for obtaining a V (velocity) and P (momentum) matrix and examine properties of both. We also consider the time dependence of the V and P matrices and show that it is consistent with either helical motion or oscillatory motion in a dimension perpendicular to that of the motion of the particle. This oscillatory motion disappears if v=0 or p=0, but there seems to be a different oscillatory motion for p=0.</p>