Abstract:
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, zero mode.
Citation:
E. G. Gelfer, A. M. Fedotov, V. D. Mur, N. B. Narozhny, “Boost modes for a massive fermion field and the Unruh quantization”, TMF, 182:3 (2015), 405–434; Theoret. and Math. Phys., 182:3 (2015), 356–380
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\paper Boost modes for a~massive fermion field and the Unruh quantization
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\pages 405--434
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\jour Theoret. and Math. Phys.
\yr 2015
\vol 182
\issue 3
\pages 356--380
\crossref{https://doi.org/10.1007/s11232-015-0268-0}
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Linking options:
https://www.mathnet.ru/eng/tmf8690
https://doi.org/10.4213/tmf8690
https://www.mathnet.ru/eng/tmf/v182/i3/p405
This publication is cited in the following 4 articles:
S. V. Popruzhenko, A. M. Fedotov, “Dynamics and radiation of charged particles in ultra-intense laser fields”, Phys. Usp., 66:5 (2023), 460–493
Barbado L.C., Barcelo C., Garay L.J., Jannes G., “Hawking versus Unruh effects, or the difficulty of slowly crossing a black hole horizon”, J. High Energy Phys., 2016, no. 10, 161
Fedotov A.M., Narozhny N.B., “Scalar and fermion representations of the Lorentz group in Minkowski plane, QFT correlators, pair creation in electric field and the Unruh effect”, Int. J. Mod. Phys. D, 25:3 (2016), 1630008
Citation in format AMSBIB
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