Strong field pair production

American Journal of Physics

Volumn 67, Issue 6, 1999, Pages 499-507

  Holstein, Barry R ^a,b  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033416063     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19313     Document Type: Article

References (27)

1. 1See, e.g., S. W. Hawking and G. F. R. Ellis, Large Scale Structure of Spacetime (Cambridge U.P., New York, 1973); J. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Spacetime (Cambridge U.P., New York, 1982).
2. 1See, e.g., S. W. Hawking and G. F. R. Ellis, Large Scale Structure of Spacetime (Cambridge U.P., New York, 1973); J. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Spacetime (Cambridge U.P., New York, 1982).
3. J. Schwinger, "On Gauge Invariance and Vacuum Polarization," Phys. Rev. 82, 664-679 (1951).
4. B. R. Holstein, "Klein's Paradox," Am. J. Phys. 66, 507-512 (1998).
5. T. Damour, Proceedings of the First Marcel Grossman Meeting on General Relativity, edited by R. Ruffini (North-Holland, Amsterdam, 1970), pp. 459-482.
6. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
7. 6See, e.g., B. R. Holstein, Topics in Advanced Quantum Mechanics (Addison-Wesley, Reading, MA, 1992), Chap. 8.
8. μ. (113)
9. course, if there exist any zero or negative eigenvalues, things must be handled more carefully - cf. S. Coleman, "Secret Symmetry: An Introduction to Spontaneous Symmetry Breakdown and Gauge Fields," in Aspects of Symmetry (Cambridge U.P., New York, 1985).
10. Note that we have denoted the transverse directions x,y collectively by the symbol ⊥.
11. A careful reader will note that the imaginary component of ζ, which corresponds to a shift in the energy per unit volume due to quantum effects, diverges. This is simply the well-known vacuum energy contribution, which is removed by renormalization of the energy zero point - cf. B. R. Holstein, Topics in Advanced Quantum Mechanics (Addison-Wesley, Reading, MA, 1992), Chap. III.6.
12. Klein, "Die Reflexion von Elektronen an eimem Potentialsprung nach der Relativistischen Dynamik von Dirac," Z. Phys. 53, 157-165 (1929). Here the translation is by V. Telegdi in unpublished lecture notes (1995).
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14. M. G. Fuda and E. Furlani, "Zitterbewegung and the Klein Paradox for Spin-Zero Particles," Am. J. Phys. 50, 545-549 (1982).
15. M. Abramowitz and J. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, DC, 1968).
16. I. S. Gradsteyn and I. M. Ryzhik, Tables of Integrals, Series and Products (Academic, New York, 1965), Vol. 9.132.1.
17. A. I. Nishikov, "Pair Production by a Constant Electric Field," Sov. Phys. JETP 30, 660-662 (1969); "Barrier Scattering in Field Theory Removal of Klein Paradox," Nucl. Phys. B 21, 346-358 (1970).
18. A. I. Nishikov, "Pair Production by a Constant Electric Field," Sov. Phys. JETP 30, 660-662 (1969); "Barrier Scattering in Field Theory Removal of Klein Paradox," Nucl. Phys. B 21, 346-358 (1970).
19. 0 is varied.
20. 0. (114)
21. See, e.g., J. F. Donoghue, E. Golowich, and B. R. Holstein, Dynamics of the Standard Model (Cambridge U.P., New York, 1992).
22. Since spin does not enter into the transmission or reflection probability, this replacement is merely a trick which removes the spin degrees of freedom from the problem.
23. D. L. Burke et al., "Positron Production in Multiphoton Light by Light Scattering," Phys. Rev. Lett. 79, 1626-1629 (1997).
24. P. C. W. Davies, "Scalar Particle Production in Schwartzchild and Rindler Metrics," J. Phys. A 8, 609-616 (1975); W. G. Unruh, "Notes on Black Hole Evaporation," Phys. Rev. D 14, 870-892 (1976).
25. P. C. W. Davies, "Scalar Particle Production in Schwartzchild and Rindler Metrics," J. Phys. A 8, 609-616 (1975); W. G. Unruh, "Notes on Black Hole Evaporation," Phys. Rev. D 14, 870-892 (1976).
26. S. W. Hawking, "Particle Creation by Black Holes." Commun. Math. Phys. 43, 199-220 (1975); P. C. W. Davies, "Quantum Field Theory in Curved Spacetime," Nature (London) 263, 377-380 (1976).
27. S. W. Hawking, "Particle Creation by Black Holes." Commun. Math. Phys. 43, 199-220 (1975); P. C. W. Davies, "Quantum Field Theory in Curved Spacetime," Nature (London) 263, 377-380 (1976).