Path integral approach to electron scattering in classical electromagnetic potential

doi:10.1088/1674-1056/25/5/050303

Abstract As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential.

Keywords: electron scattering path integral approach quantum field theory

Received: 23 August 2015
Revised: 18 December 2015
Accepted manuscript online:

PACS:	03.65.-w	(Quantum mechanics)
	03.70.+k	(Theory of quantized fields)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11374360, 11405266, and 11505285) and the National Basic Research Program of China (Grant No. 2013CBA01504).

Corresponding Authors: Chuang Xu, Ying-Jun Li
E-mail: xu.chuang.phy@gmail.com;lyj@aphy.iphy.ac.cn

Cite this article:

Chuang Xu(许闯), Feng Feng(冯锋), Ying-Jun Li(李英骏) Path integral approach to electron scattering in classical electromagnetic potential 2016 Chin. Phys. B 25 050303

[1]	Dirac P A M 1933 Physik. Zeits. Sowjetunion 3 64
[2]	Feynman R P 1948 Rev. Mod. Phys. 20 367
[3]	Feynman R P 1963 Acta Phys. Pol. 24 697
[4]	Faddeev L D and Popov V N 1967 Phys. Lett. B 25 29
[5]	Hooft G't 1971 Nucl. Phys. B 35 167
[6]	Englert F and Brout R 1964 Phys. Rev. Lett. 13 321
[7]	Higgs P W 1964 Phys. Rev. Lett. 13 508
[8]	Higgs P W 1966 Phys. Rev. 145 1156
[9]	Weinberg S 1976 Phys. Rev. Lett. 36 294
[10]	Yanovsky V, Chvykov V, Kalinchenko G, Rousseau P, Planchon T, Matsuoka T, Maksimchuk A, Nees J, Cheriaux G, Mourou G and Krushelnick K 2008 Opt. Express 16 2109
[11]	Faure J, Glinec Y, Pukhov A, Kiselev S, Gordienko S, Lefebvre E, Rousseau J P, Burgy F and Malka V 2004 Nature 431 541
[12]	Faure J, Rechatin C, Norlin A, Lifschitz A, Glinec Y and Malka V 2006 Nature 444 737
[13]	Schoenlein R W, Leemans W P, Chin A H, Volfbeyn P, Glover T E, Balling P, Zolotorev M, Kim K J, Chattopadhyay S and Shank C V 1996 Science 274 236
[14]	Tomassini P, Giulietti A, Giulietti D and Gizzi L A 2005 Appl. Phys. B 80 419
[15]	Schwoerer H, Liesfeld B, Schlenvoigt H P, Amthor K U and Sauerbrey R 2006 Phys. Rev. Lett. 96 014802
[16]	Jochmann A, Irman A, Bussmann M, Couperus J P, Cowan T E, Debus A D, Kuntzsch M, Ledingham K W D, Lehnert U, Sauerbrey R, Schlenvoigt H P, Seipt D, Stohlker Th, Thorn D B, Trotsenko S, Wagner A and Schramm U 2013 Phys. Rev. Lett. 111 114803
[17]	Hartemann F V and Kerman A K 1996 Phys. Rev. Lett. 76 624
[18]	Bula C, McDonald K T, Prebys E J, Bamber C, Boege S, Kotseroglou T, Melissinos A C, Meyerhofer D D, Ragg W, Burke D L, Field R C, Horton-Smith G, Odian A C, Spencer J E, Walz D, Berridge S C, Bugg W M, Shmakov K and Weidemann A W 1996 Phys. Rev. Lett. 76 3116
[19]	Boca M and Florescu V 2009 Phys. Rev. A 80 053403
[20]	Seipt D and Kampfer B 2011 Phys. Rev. A 83 022101
[21]	Liang G H, Lü Q Z, Teng A P and Li Y J 2014 Chin. Phys. B 23 054103
[22]	Fan H Y, Zhang P F and Wang Z 2015 Chin. Phys. B 24 050303
[23]	Peskin M E and Schroeder D V 1995 An Introduction to Quantum Field Theory (Westview Press)
[24]	Lehmann H, Symanzik K and Zimmermann W 1955 Nuovo Cimento 1 205
[25]	Leo S D and Rotelli P 2009 Eur. Phys. J. C 62 793
[26]	Klein O 1929 Z. Phys. 53 157
[27]	Nikishov A I 1970 Nucl. Phys. B 21 346
[28]	Hansen A and Ravndal F 1981 Phys. Scr. 23 1033
[29]	McKellar B H J and Stephenson G J 1987 Phys. Rev. A 36 2566
[30]	Manogue C A 1988 Ann. Phys. 181 261
[31]	Dombey N and Calogeracos A 1999 Phys. Rep. 315 41
[32]	Katsnelson M I, Novoselov K S and Geim A K 2006 Nat. Phys. 2 620

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