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In quantum we have a density matrix for the spin states. The density matrix allows us to specify both polarized states, but also various levels of polarization.

The relativistic version of the spin vector is the angular momentum 4-tensor, with 3 spin components and 3 other components. These other guys (I call them the 'intrinsic boost momentum') have states that are going forwards or backwards at the speed of light. Along with the spin, they are related to the chirality.

But what I'd like to see is a development of a density matrix for this instrinsic boost momentum.

Has anyone come across of nice explanation of this?

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A density matrix is a representation of a quantum states in a particular basis. So a density matrix for the spin states would be expressed in a basis consisting of the eigenstates of the angular momentum operator.

One can therefore consider any set of eigenstates to represent a density matrix in that basis. In the relativistic context, I would imagine that one can consider the eigenstates of the Lorentz boosts (not sure what these would look like) and then express a density matrix in this basis.

BTW, density matrices are usually used to take care of the possibility of having mixed states. If one knows that the states are pure states then one can just as well consider the quantum states as a superposition of eigenstates, denoted by ket vectors.

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