Treatment of Spin-1/2 Particle in Interaction with a Time-Dependent Magnetic Field by the Fermionic Coherent-State Path-Integral Formalism

We consider a spin-1/2 particle interacting with a time-dependent magnetic field using path integral formalism. The propagator is first of all written in the standard form replacing the spin by two fermionic oscillators via the Schwinger model. The propagator
is then exactly determined, thanks to a simple transformation, and the transition probability is deduced.

• Aouachria Mekki

• Path integral
• formalism
• Propagator.

[1] C. Grosche and F. Steiner, Handbook of Feynman Path Integrals, (Springer-Verlag Berlin 1998).
[2] I. I. Rabi, Phys. Rev. 51, 652 (1936).
[3] M. J. Tahmasebi and Y. Sobouti, Mod. Phys. Lett. B 5, 1919 (1991).
[4] M. J. Tahmasebi and Y. Sobouti, Mod. Phys. Lett. B 6, 1255 (1991).
[5] C. L¨ammerzahl, C. J. Bord´e, Phys. Lett. A 203, 59 (1995).
[6] L. Qiong-Gui, Phys. Lett. A 342, 67 (2005).
[7] M. Calvo, S. Codriansky, J. Math. Phys. 24, 553 (1983).
[8] A. O. Barut and H. Beker, Eur. Phys. Lett. 14, 197 (1991).
[9] M. Mijatovi´c, C. Ivanovski, B. Veljanoski and Trenˇcevski K, Z. Phys. A 345, 65 (1993).
[10] S. Codriansky, P. Cordero and S. Salamo, Z. Phys. A 353, 341(1995).
[11] T. Boudjedaa, A. Bounames, Kh. Nouicer, L. Chetouani and T. F. Hammann, Phys. Scripta. 54, 225 (1996).
[12] T. Boudjedaa, A. Bounames, Kh. Nouicer, L. Chetouani and T. F. Hammann, Phys. Scripta. 56, 545 (1998).
[13] A. Merdaci, T. Boudjedaa, and L. Chetouani, Phys. Scripta. 64, 15 (2001).
[14] A. Merdaci, T. Boudjedaa, and L. Chetouani, Czech. J. Phys. 51, 865 (2001).
[15] A. Merdaci, T. Boudjedaa, and L. Chetouani, Eur. Phys. J. C 22, 585 (2001).
[16] Kh. Nouicer, L. Chetouani, Phys. Lett. A 281, 218 (2001).
[17] M. Aouachria, L. Chetouani, Eur. Phys. J. C 25, 333 (2002).
[18] M. Aouachria, L. Chetouani, Chinese. J. Phys. 40, 496 (2002).
[19] M. Aouachria, Chinese. J. Phys. 49, 689 (2011).
[20] M. Aouachria, J. Phys. Conf. Ser. 435, 012021 (2013).
[21] M. Nakamura , K. Kazuo Kitahara, J. Phys. Soc. of Japan. 60, 1388 (1991).