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TMF, 1976, Volume 26, Number 1, Pages 16–34 (Mi tmf3163)  

This article is cited in 7 scientific papers (total in 7 papers)

Solutions of the Klein-Gordon and Dirac equations for a particle in a constant electric field and a plane electromagnetic wave propagating along the field

N. B. Narozhnyi, A. I. Nikishov

Abstract: A complete set of solutions is found to the Klein–Gordon and Dirac equations for the case of a constant (in space and time) electric field along which a plane electromagnetic wave propagates. The solutions are labeled by the numbers $p_1$, $p_2$, $p_3$, which become the conserved three-momentum when the field of the wave is switched off. These solutions are related by an integral transformation to previously obtained solutions labeled by conserved components of the momentum: $p_1$, $p_2$, $p_-=p_0-p_3$. In contrast to these last solutions, the $\psi_{p_3}$-solutions arc everywhere finite and can be explicitly classified with respect to the sign of the “frequency” as $x_0\to\pm\infty$. It is also shown that the solutions $\psi_{p_-}$ too can be classified with respect to the sign of the “frequency”. This means that they can be used in the usual manner to describe matrix elements. Propagators are obtained in the Fock–Schwinger and Feynman representations. It is shown that not only the total but also the differential probabilities of pair creation by the field are independent of the field of the wave if they are expressed in terms of Lorentz and gauge-invariant quantities.

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English version:
Theoretical and Mathematical Physics, 1976, 26:1, 9–20

Received: 06.03.1975

Citation: N. B. Narozhnyi, A. I. Nikishov, “Solutions of the Klein-Gordon and Dirac equations for a particle in a constant electric field and a plane electromagnetic wave propagating along the field”, TMF, 26:1 (1976), 16–34; Theoret. and Math. Phys., 26:1 (1976), 9–20

Citation in format AMSBIB
\by N.~B.~Narozhnyi, A.~I.~Nikishov
\paper Solutions of the Klein-Gordon and Dirac equations for a~particle in a~constant electric field and a~plane electromagnetic wave propagating along the field
\jour TMF
\yr 1976
\vol 26
\issue 1
\pages 16--34
\jour Theoret. and Math. Phys.
\yr 1976
\vol 26
\issue 1
\pages 9--20

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    This publication is cited in the following articles:
    1. A. A. Lobashev, V. M. Mostepanenko, “Quantum effects in nonlinear insulating materials in the presence of a nonstationary electromagnetic field”, Theoret. and Math. Phys., 86:3 (1991), 303–309  mathnet  crossref
    2. A. A. Lobashov, V. M. Mostepanenko, “Quantum effects associated with parametric generation of light and the theory of squeezed states”, Theoret. and Math. Phys., 88:3 (1991), 913–925  mathnet  crossref  isi
    3. A. I. Nikishov, “Equivalent Sets of Solutions of the Klein–Gordon Equation with a Constant Electric Field”, Theoret. and Math. Phys., 136:1 (2003), 958–969  mathnet  crossref  crossref  mathscinet  isi
    4. Merad M., Zeroual F., Falek M., “Relativistic Particle in Electromagnetic Fields with a Generalized Uncertainty Principle”, Mod. Phys. Lett. A, 27:15 (2012), 1250080  crossref  isi
    5. E. G. Gelfer, A. M. Fedotov, V. D. Mur, N. B. Narozhny, “Boost modes for a massive fermion field and the Unruh quantization”, Theoret. and Math. Phys., 182:3 (2015), 356–380  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. Tilbi A., Merad M., Boudjedaa T., “Particles of Spin Zero and 1/2 in Electromagnetic Field With Confining Scalar Potential in Modified Heisenberg Algebra”, Few-Body Syst., 56:2-3 (2015), 139–147  crossref  isi
    7. 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
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