Kinetic momentum

From Wikipedia, the free encyclopedia

This article appears to contradict itself. Please see the discussion on the talk page.

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

$\mathbf{p} = \gamma m \mathbf{v}$

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

$\pi = \mathbf{p} - {q\mathbf{A} \over c}$