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 TMF, 1974, Volume 19, Number 1, Pages 83–96 (Mi tmf3567)

Creation of fermion pairs in a homogeneous alternating external field

A. M. Perelomov

Abstract: Group-theoretical aspects of the problem of fermion pair creation in a homogeneous alternating external field are considered. It is shown that the dynamical symmetry group of this problem is $SU(2N)$ ($N=2s+1$, where $s$ is the particle spin) and that the state of the system that arises during evolution is a generalized coherent state associated with this group. The probability of pair creation is given by the square of the modulus of the matrix element of a definite representation of $SU(2N)$. For particles of spin 1/2 in certain cases the symmetry group reduces to $SU(2)\times SU(2)$.

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English version:
Theoretical and Mathematical Physics, 1974, 19:1, 368–377

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Citation: A. M. Perelomov, “Creation of fermion pairs in a homogeneous alternating external field”, TMF, 19:1 (1974), 83–96; Theoret. and Math. Phys., 19:1 (1974), 368–377

Citation in format AMSBIB
\Bibitem{Per74} \by A.~M.~Perelomov \paper Creation of fermion pairs in a~homogeneous alternating external field \jour TMF \yr 1974 \vol 19 \issue 1 \pages 83--96 \mathnet{http://mi.mathnet.ru/tmf3567} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=468752} \transl \jour Theoret. and Math. Phys. \yr 1974 \vol 19 \issue 1 \pages 368--377 \crossref{https://doi.org/10.1007/BF01037193} 

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This publication is cited in the following articles:
1. A. A. Grib, V. M. Mostepanenko, V. M. Frolov, “Creation and scattering of particles by a nonstationary electromagnetic field in the canonical formalism”, Theoret. and Math. Phys., 26:2 (1976), 148–155
2. V. P. Karassiov, L. A. Shelepin, “Theory of Generalized coherent states of the groups $SU_n$”, Theoret. and Math. Phys., 45:1 (1980), 879–886
3. V. M. Mostepanenko, “Particle creation and vacuum polarization by a nonstationary electric field”, Theoret. and Math. Phys., 45:2 (1980), 983–991
4. 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
5. 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
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