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TMF, 2015, Volume 182, Number 3, Pages 405–434 (Mi tmf8690)  

This article is cited in 3 scientific papers (total in 3 papers)

Boost modes for a massive fermion field and the Unruh quantization

E. G. Gelfer*, A. M. Fedotov, V. D. Mur, N. B. Narozhny

National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russia

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

Funding Agency Grant Number
Russian Foundation for Basic Research 13-02-00372
Ministry of Education and Science of the Russian Federation НШ-4829.2014.2

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf8690

Full text: PDF file (700 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2015, 182:3, 356–380

Bibliographic databases:

PACS: 03.70.+k, 11.10.-z, 11.30.Cp
Received: 02.04.2014
Revised: 22.05.2014

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

Citation in format AMSBIB
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\paper Boost modes for a~massive fermion field and the Unruh quantization
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\yr 2015
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\issue 3
\pages 405--434
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  crossref  mathscinet  zmath  isi  scopus
    2. Barbado L.C., Barcelo C., Garay L.J., Jannes G., “A tensorial description of particle perception in black-hole physics”, Phys. Rev. D, 94:6 (2016), 064004  crossref  mathscinet  isi  elib  scopus
    3. 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  crossref  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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