Kinetic momentum
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In relativistic mechanics, kinetic momentum is defined as the difference between total momentum and potential momentum. Kinetic momentum is Lorentz gauge covariant: meaning that it is invariant under Lorentz transformations. Therefore the kinetic momentum is used to construct the relativistic Hamiltonian.
Kinetic momentum may be given by
where γ is the Lorentz factor. For the case of a particle with charge q in an electromagnetic field whose vector potential is A, though, the kinetic momentum may be given by
where c is the speed of light.
