Geodesic
Boost modes for a~massive fermion field and the Unruh quantization
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 3, pp. 405-434

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We show that the Wightman function of a free quantum field generates any complete set of solutions of the relativistic wave equations. Using this approach, we construct the complete set of solutions of the two-dimensional Dirac equation consisting of eigenfunctions of the generator of Lorentz rotations (boost operator). We show that at the surface of the light cone, the boost modes for a fermion field contain the Gelfand delta function of a complex argument. Because of the presence of such a singularity, excluding even a single mode with an arbitrary value of the boost quantum number makes the set of boost modes incomplete. This results in the nonapplicability of the Unruh quantization scheme to a massive fermion field in the two-dimensional Minkowski space–time. Hence, in full accordance with the boson case, the Unruh procedure for a fermion field cannot be used to prove the existence of the Unruh effect.
Keywords: boost symmetry, fermion field, Wightman function
Mots-clés : zero mode. 
@article{TMF_2015_182_3_a2,
     author = {E. G. Gelfer and A. M. Fedotov and V. D. Mur and N. B. Narozhny},
     title = {Boost modes for a~massive fermion field and the {Unruh} quantization},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {405--434},
     publisher = {mathdoc},
     volume = {182},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_3_a2/}
}
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E. G. Gelfer; A. M. Fedotov; V. D. Mur; N. B. Narozhny. Boost modes for a~massive fermion field and the Unruh quantization. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 3, pp. 405-434. http://geodesic.mathdoc.fr/item/TMF_2015_182_3_a2/