Angular momentum operator for Dirac equation

Question

The orbital angular momentum operator is given by
$$L_i=epsilon_{ijk}x_j p_k$$
where $x$ and $p$ are the position and momentum operators.
In the Dirac equation, the hamiltonian operator is a 4x4 matrix. Will $L_i$ then also be a 4x4 matrix, which is given by $$L_i=epsilon_{ijk}x_j p_k I$$
where $I$ is the identitiy matrix? Or is it just still $L_i=epsilon_{ijk}x_j p_k$ without the identity matrix?

Thomas Fritsch · Accepted Answer

Formally all linear operators are $4times 4$ matrices,
because they need to transform Dirac-spinors to Dirac-spinors.
Therefore all those operators, which don't mix the components of Dirac-spinors
(like $x_i$, $p_i$, $L_i$), contain $I$ (the $4times 4$ identity matrix)
as a factor.

Angular momentum operator for Dirac equation

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