Square-roots,internal symmetries,and fermion field quantization

It is observed that the complex square-root of the hermitian matrix σ^μ p _μ associated with a physical four-momentum admits Lorentz-independent unitary transformations that may be related to the internal symmetries of hadrons. An operator-valued square-root of the Hilbert space inner product in relativistic one-electron theory brings in fermion field quantization conditions as a direct concomitant of its linearity and hermicity properties.