  We have shown that Wightman function of a free quantum field generates any
complete set of solutions of relativistic wave equations. Using this approach
we have constructed the complete set of solutions to 2d Dirac equation
consisting of eigenfunctions of the generator of Lorentz rotations (boost
operator). It is shown that at the surface of the light cone the boost modes
for a fermion field contain $\delta$-function of a complex argument. Due to the
presence of such singularity exclusion even of a single mode with an arbitrary
value of the boost quantum number makes the set of boost modes incomplete.
