Algebra of Physical Space - Classical Spinor

Classical Spinor

The differential equation of the Lorentz rotor that is consistent with the Lorentz force is

\frac{d \Lambda}{ d \tau} = \frac{e}{2mc} F \Lambda,

such that the proper velocity is calculated as the Lorentz transformation of the proper velocity at rest

u = \Lambda \Lambda^\dagger,

which can be integrated to find the space-time trajectory with the additional use of

\frac{d x}{ d \tau} = u

Read more about this topic:  Algebra Of Physical Space

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