Fourier transform of the free Dirac equation

In the following, the Fourier transformation (24) will be denoted by T, that is A Fourier transformation of the stationary free Dirac equation 

The 4x4 matrix h(p) is Hermitian for each p G (that is, h(p) = h(p))- A Hermitian matrix can always be diagonalized by a unitary transformation u(p) 

This matrix is indeed diagonal in the standard representation. (But the formulas 

The set of eigenvalues E p) for all p is called the spectrum of the free Dirac operator and denoted by a Ho), 

This is the set of all energies for which the free stationary Dirac equation has plane-wave like solutions (out of which square-integrable wave packets can be formed). The spectrum a Ho) is the continuum of all real numbers except the numbers in the spectral gap, the open interval (—mc, mc ). 

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