Geodesic
Comparative analysis of direct and “step-by-step" Foldy–Wouthuysen transformation methods
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 2, pp. 189-204 Cet article a éte moissonné depuis la source Math-Net.Ru

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Relativistic methods for the Foldy–Wouthuysen transformation of the “step-by-step” type already at the first step give an expression for the Hamilton operator not coinciding with the exact result determined by the Eriksen method. The methods agree for the zeroth and first orders in the Planck constant terms but do not agree for the second and higher-order terms. We analyze the benefits and drawbacks of various methods and establish their applicability boundaries.
Keywords: Foldy–Wouthuysen transformation, unitary transformation, relativistic quantum mechanics. 
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A. Ya. Silenko. Comparative analysis of direct and “step-by-step" Foldy–Wouthuysen transformation methods. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 2, pp. 189-204. http://geodesic.mathdoc.fr/item/TMF_2013_176_2_a1/

[1] L. L. Foldy, S. A. Wouthuysen, Phys. Rev. (2), 78:1 (1950), 29–36 | DOI | Zbl

[2] T. D. Newton, E. P. Wigner, Rev. Modern Phys., 21:3 (1949), 400–406 | DOI | Zbl

[3] A. J. Silenko, J. Math. Phys., 44:7 (2003), 2952–2966 | DOI | MR | Zbl

[4] J. P. Costella, B. H. J. McKellar, Amer. J. Phys., 63:12 (1995), 1119–1121 | DOI | MR | Zbl

[5] A. Ya. Silenko, Pisma v EChAYa, 10 (2013), 144–148

[6] V. G. Baryshevsky, J. Phys. G, 35:3 (2008), 035102, 23 pp. | DOI

[7] A. J. Silenko, Phys. Rev. C, 80:4 (2009), 044315, 5 pp. | DOI

[8] V. G. Baryshevsky, A. J. Silenko, J. Phys.: Conf. Ser., 295:1 (2011), 012034, 5 pp., arXiv: 1011.2352 | DOI

[9] V. P. Neznamov, A. J. Silenko, J. Math. Phys., 50:12 (2009), 122302, 15 pp., arXiv: 0906.2069 | DOI | MR | Zbl

[10] E. Eriksen, M. Korlsrud, Nuovo Cimento Suppl., 18 (1960), 1–39 | DOI | MR

[11] E. Eriksen, Phys. Rev. (2), 111:3 (1958), 1011–1016 | DOI | MR | Zbl

[12] F. Hausdorff, Ber. über die Verhandlungen der Königl. Sächs. Ges. der Wiss. zu Leipzig. Math.-phys. Klasse, 58 (1906), 106–169 | Zbl

[13] S. Stephani, Ann. Phys. (Berlin), 470:1–2 (1965), 12–16 | DOI | Zbl

[14] V. P. Neznamov, VANT. Ser. teor. prikl. fiz., 2 (1988), 21–27

[15] V. P. Neznamov, EChAYa, 37:1 (2006), 151–182, arXiv: hep-th/0411050 | DOI

[16] E. de Vries, J. E. Jonker, Nucl. Phys. B, 6:3 (1968), 213–225 | DOI

[17] E. I. Blount, Phys. Rev. (2), 128:5 (1962), 2454–2458 | DOI | Zbl

[18] A. J. Silenko, Phys. Rev. A, 77:1 (2008), 012116, 7 pp., arXiv: 0710.4218 | DOI | MR

[19] P. Gosselin, A. Bérard, H. Mohrbach, Europ. Phys. J. B, 58:2 (2007), 137–148 | DOI | MR | Zbl

[20] P. Gosselin, A. Berard, H. Mohrbach, Phys. Lett. A, 368:5 (2007), 356–361, arXiv: hep-th/0604012 | DOI | MR | Zbl

[21] P. Gosselin, J. Hanssen, H. Mohrbach, Phys. Rev. D, 77:8 (2008), 085008, 11 pp., arXiv: cond-mat/0611628 | DOI

[22] P. Gosselin, H. Mohrbach, Europ. Phys. J. C, 64:3 (2009), 495–527, arXiv: 0801.0940 | DOI | MR | Zbl

[23] E. de Vries, Fortsch. Phys., 18:4 (1970), 149–182 | DOI

[24] A. Ya. Silenko, TMF, 112:1 (1997), 161–169 | DOI | DOI | Zbl

[25] T. A. Osborn, F. H. Molzahn, Ann. Phys., 241:1 (1995), 79–127, arXiv: hep-th/9409120 | DOI | MR | Zbl

[26] A. Ya. Silenko, TMF, 105:1 (1995), 46–54 | DOI | MR | Zbl

[27] V. B. Berestetskii, L. D. Landau, ZhETF, 19 (1949), 673–679

[28] A. I. Akhiezer, V. B. Berestetskii, Kvantovaya elektrodinamika, Nauka, M., 1969 | MR | Zbl

[29] K. Y. Bliokh, Europhys. Lett., 72:1 (2005), 7–13 ; Phys. Lett. A, 351:3 (2006), 123–124, arXiv: cond-mat/0507499 | DOI | MR | DOI | MR | Zbl

[30] P. Gosselin, A. Berard, H. Mohrbach, S. Ghosh, Europ. Phys. J. C, 59:4 (2009), 883–889 | DOI

[31] K. M. Case, Phys. Rev., 95:5 (1954), 1323–1328 | DOI | MR | Zbl

[32] W. Tsai, Phys. Rev. D, 7:6 (1973), 1945–1948 | DOI

[33] A. Ya. Silenko, ZhETF, 114 (1998), 448–457

[34] I. M. Ternov, V. G. Bagrov, V. Ch. Zhukovskii, Vestn. Mosk. un-ta. Ser. 3. Fiz., astr., 7:1 (1966), 30–36

[35] A. J. Silenko, Pisma v EChAYa, 5:6 (2008), 842–850

[36] M. Taketani, S. Sakata, Proc. Phys. Math. Soc. Japan, 22 (1940), 757–770 | MR

[37] J. A. Young, S. A. Bludman, Phys. Rev., 131:5 (1963), 2326–2334 | DOI

[38] A. J. Silenko, Europ. Phys. J. C, 57:3 (2008), 595–599, arXiv: 0803.3577 | DOI | MR | Zbl

[39] A. J. Silenko, Analysis of wave equations for spin-1 particles interacting with an electromagnetic field, arXiv: hep-th/0404074

[40] A. Ya. Silenko, ZhETF, 123:5 (2003), 883–890 | MR

[41] W. Tsai, A. Yildiz, Phys. Rev. D, 4:12 (1971), 3643–3648 | DOI

[42] T. Goldman, W. Tsai, A. Yildiz, Phys. Rev. D, 5:8 (1972), 1926–1930 | DOI

[43] B. Vijayalakshmi, M. Seetharaman, P. M. Mathews, J. Phys. A, 12:5 (1979), 665–677 | DOI | MR

[44] Y. N. Obukhov, A. J. Silenko, O. V. Teryaev, Phys. Rev. D, 80:6 (2009), 064044, 10 pp. | DOI

[45] Y. N. Obukhov, A. J. Silenko, O. V. Teryaev, Phys. Rev. D, 84:2 (2011), 024025, 10 pp., arXiv: 1106.0173 | DOI