Geodesic
Polarization of vacuum by an external magnetic field in the $(2+1)$-dimensional quantum electrodynamics with a nonzero fermion density
Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 1, pp. 132-151 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Green's function of the Dirac equation with an external stationary homogeneous magnetic field in the $(2+1)$-dimensional quantum electrodynamics ($\mathrm{QED}_{2+1}$) with a nonzero fermion density is constructed. An expression for the polarization operator in an external stationary homogeneous magnetic field with a nonzero chemical potential is derived in the one-loop $\mathrm{QED}_{2+1}$ approximation. The contribution of the induced Chern–Simons term to the polarization operator and the effective Lagrangian for the fermion density corresponding to the occupation of $n$ relativistic Landau levels in an external magnetic field are calculated. An expression of the induced Chern–Simons term in a magnetic field for the case of a finite temperature and a nonzero chemical potential is obtained. 
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V. R. Khalilov. Polarization of vacuum by an external magnetic field in the $(2+1)$-dimensional quantum electrodynamics with a nonzero fermion density. Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 1, pp. 132-151. http://geodesic.mathdoc.fr/item/TMF_2000_125_1_a5/

[1] A. M. J. Schakel, G. W. Semenoff, Phys. Rev. Lett., 66 (1991), 2653 | DOI

[2] R. E. Prange, S. M. Girvin (eds.), The Quantum Hall Effect, 2nd ed., Springer-Verlag, New York, 1990 | MR

[3] F. Wilczek, Fractional Statistics and Anyon Superconductivity, World Scientific, Singapore, 1990 | MR | Zbl

[4] A. M. J. Schakel, Phys. Rev. D, 43 (1991), 1428 | DOI

[5] A. Neagu, A. M. J. Schakel, Phys. Rev. D, 48 (1993), 1785 | DOI

[6] J. M. Leinaas, J. Myrheim, Nuovo Cim. B, 37 (1977), 1 | DOI

[7] G. A. Goldin, R. Menikoff, D. H. Sharp, J. Math. Phys., 22 (1981), 1664 | DOI | MR

[8] F. Wilczek, Phys. Rev. Lett., 48 (1982), 1144 ; 49, 957 | DOI | MR | DOI

[9] Y. Hosotani, Phys. Lett. B, 319 (1993), 332 ; Phys. Rev. D, 51 (1995), 2022 | DOI | DOI

[10] V. R. Khalilov, C. L. Ho, Mod. Phys. Lett. A, 13 (1998), 615 | DOI

[11] V. R. Khalilov, TMF, 119 (1999), 105 ; C. L. Ho, V. R. Khalilov, Phys. Rev. A, 61 (2000), 032104 | DOI | Zbl | DOI

[12] A. V. Turbiner, Commun. Math. Phys., 118 (1988), 467 ; M. A. Shifman, A. V. Turbiner, Commun. Math. Phys., 126 (1989), 347 | DOI | MR | Zbl | DOI | MR | Zbl

[13] V. R. Khalilov, C. L. Ho, Phys. Rev. D, 60 (1999), 033003 | DOI

[14] V. I. Ritus, ZhETF, 57 (1969), 2176

[15] I. A. Batalin, A. E. Shabad, ZhETF, 60 (1971), 894 | MR

[16] A. A. Grib, S. G. Mamaev, V. M. Mostepanenko, Vakuumnye kvantovye effekty v silnykh polyakh, Energoatomizdat, M., 1988

[17] V. Zeitlin, Phys. Lett. B, 352 (1995), 422 | DOI

[18] V. I. Ritus, Tr. FIAN SSSR, 111, 1979, 5 | MR

[19] S. Deser, R. Jackiw, S. Templeton, Phys. Rev. Lett., 48 (1982), 975 | DOI

[20] I. M. Ternov, V. Ch. Zhukovskii, A. V. Borisov, Kvantovye protsessy v silnom vneshnem pole, MGU, M., 1989

[21] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, T. 2, Nauka, M., 1974 | MR

[22] V. A. Fock, Sow. Phys., 12 (1937), 404 | Zbl

[23] J. Schwinger, Phys. Rev., 82 (1951), 664 | DOI | MR | Zbl

[24] V. R. Khalilov, TMF, 121 (1999), 412 | DOI | Zbl

[25] E. M. Lifshits, L. P. Pitaevskii, Statisticheskaya fizika, Ch. 2, Nauka, M., 1978

[26] A. E. Shabad, Osobennosti polyarizatsionnogo operatora fotona v magnitnom pole, Preprint FIAN No 60, FIAN, M., 1974

[27] A. E. Lobanov, V. R. Khalilov, ZhETF, 77 (1979), 548

[28] V. B. Berestetskii, E. M. Lifshits, L. P. Pitaevskii, Kvantovaya elektrodinamika, Nauka, M., 1980 | MR

[29] I. S. Gradshtein, I. M. Ryzhik, Tablitsy integralov, summ, ryadov i proizvedenii, GIFML, M., 1963 | MR

[30] A. Redlich, Phys. Rev. D, 29 (1984), 2366 | DOI | MR

[31] N. N. Bogolyubov, D. V. Shirkov, Kvantovye polya, Nauka, M., 1980 | MR | Zbl

[32] T. Bernstein, A. Lee, Phys. Rev. D, 32 (1985), 1020 ; S. Coleman, B. Hill, Phys. Lett. B, 159 (1985), 184 ; Y. Nagahami, Z. Phys. C, 37 (1986), 583 | DOI | DOI | DOI