Geodesic
Hamilton operator and the semiclassical limit for scalar particles in
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 398-411 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We successively apply the generalized Case–Foldy–Feshbach–Villars (CFFV) and the Foldy–Wouthuysen (FW) transformation to derive the Hamiltonian for relativistic scalar particles in an electromagnetic field. In contrast to the original transformation, the generalized CFFV transformation contains an arbitrary parameter and can be performed for massless particles, which allows solving the problem of massless particles in an electromagnetic field. We show that the form of the Hamiltonian in the FW representation is independent of the arbitrarily chosen parameter. Compared with the classical Hamiltonian for point particles, this Hamiltonian contains quantum terms characterizing the quadrupole coupling of moving particles to the electric field and the electric and mixed polarizabilities. We obtain the quantum mechanical and semiclassical equations of motion of massive and massless particles in an electromagnetic field.
Mots-clés : Klein–Gordon equation, scalar particle
Keywords: Case–Foldy–Feshbach–Villars transformation, Foldy–Wouthuysen transformation, electromagnetic interaction. 
@article{TMF_2008_156_3_a5,
     author = {A. Ya. Silenko},
     title = {Hamilton operator and the~semiclassical limit for scalar particles in},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {398--411},
     year = {2008},
     volume = {156},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a5/}
}
TY  - JOUR
AU  - A. Ya. Silenko
TI  - Hamilton operator and the semiclassical limit for scalar particles in
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2008
SP  - 398
EP  - 411
VL  - 156
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a5/
LA  - ru
ID  - TMF_2008_156_3_a5
ER  - 
%0 Journal Article
%A A. Ya. Silenko
%T Hamilton operator and the semiclassical limit for scalar particles in
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2008
%P 398-411
%V 156
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a5/
%G ru
%F TMF_2008_156_3_a5
A. Ya. Silenko. Hamilton operator and the semiclassical limit for scalar particles in. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 398-411. http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a5/

[1] R. J. Duffin, Phys. Rev. (2), 54:12 (1938), 1114–1114 | DOI | Zbl

[2] N. Kemmer, Proc. Roy. Soc. Edinburgh Sect. A, 173:952 (1939), 91–116 | DOI | MR | Zbl

[3] G. Petiau, Contribution a la theorie des equations d'ondes corpusculaires, Acad. Roy. Belg. Cl. Sci. Mem. Collect. 8$^\circ$ (3), 16, no. 2, 1936 | Zbl

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

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

[6] A. Accioly, H. Blas, Phys. Rev. D, 66:6 (2002), 067501 ; Modern Phys. Lett. A, 18:12 (2003), 867–873 | DOI | DOI | MR | Zbl

[7] A. Ya. Silenko, YaF, 64:5 (2001), 1048–1053 | DOI

[8] K. M. Case, Phys. Rev. (2), 95:5 (1954), 1323–1328 | DOI | MR | Zbl

[9] L. L. Foldy, Phys. Rev. (2), 102:2 (1956), 568–581 | DOI | MR | Zbl

[10] H. Feshbach, F. Villars, Rev. Modern Phys., 30:1 (1958), 24–45 | DOI | MR | Zbl

[11] M. Nowakowski, Phys. Lett. A, 244:5 (1998), 329–337 | DOI | MR | Zbl

[12] B. M. Pimentel, V. Ya. Fainberg, TMF, 124:3 (2000), 445–462 | DOI | MR | Zbl

[13] V. Ya. Fainberg, B. M. Pimentel, Phys. Lett. A, 271:1–2 (2000), 16–25 | DOI | MR | Zbl

[14] I. V. Kanatchikov, Rept. Math. Phys., 46:1–2 (2000), 107–112 | DOI | MR | Zbl

[15] J. T. Lunardi, B. M. Pimentel, R. G. Teixeira, “Duffin–Kemmer–Petiau equation in Riemannian space-times”, Geometrical Aspects of Quantum Fields (Londrina, 2000), eds. A. A. Bytsenko, A. E. Golcalves, B. M. Pimentel, World Scientific, Singapore, 2000, 111–127 | MR | Zbl

[16] T. Tanaka, A. Suzuki, M. Kimura, Z. Phys. A, 353:1 (1995), 79–85 | DOI

[17] M. Taketani, S. Sakata, Proc. Phys. Math. Soc. Japan, 22 (1940), 757–770 ; Progr. Theoret. Phys., 1:Suppl. 1 (1955), 84–97 | MR | Zbl | DOI

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

[19] A. S. Davydov, Kvantovaya mekhanika, Fizmatgiz, M., 1963 | MR | MR

[20] A. Mostafazadeh, Czechoslovak J. Phys., 53:11 (2003), 1079–1084 | DOI | MR

[21] A. Mostafazadeh, J. Phys. A, 31:38 (1998), 7829–7845 ; Ann. Phys., 309:1 (2004), 1–48 | DOI | MR | Zbl | DOI | MR | Zbl

[22] R. Casana, M. Pazetti, B. M. Pimentel, J. S. Valverde, Pseudoclassical mechanics for the spin 0 and 1 particles, , 2005 arXiv: hep-th/0506193 | MR

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

[24] W. Pauli, Rev. Modern Phys., 13:3 (1941), 203–232 | DOI | Zbl

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

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

[27] Dzh. D. Berken, S. D. Drell, Relyativistskaya kvantovaya teoriya. T. 1. Relyativistskaya kvantovaya mekhanika, Nauka, M., 1978 | MR | MR | Zbl

[28] A. I. Akhiezer, V. B. Berestetskii, Kvantovaya elektrodinamika, 3-e izd., Nauka, M., 1969 | MR | MR

[29] J. G. Körner, G. Thompson, Phys. Lett. B, 264:1–2 (1991), 185–192 | DOI

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

[31] A. J. Silenko, Analysis of wave equations for spin-1 particles interacting with an electromagnetic field, , 2004 arXiv: hep-th/0404074

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

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

[34] A. J. Silenko, O. V. Teryaev, Phys. Rev. D, 71:6 (2005), 064016 | DOI | MR

[35] A. G. Nikitin, V. I. Fuschich, TMF, 34:3 (1978), 319–333 | DOI | MR