Estudio del número de pares creados por un campo eléctrico*
J. Haro
Dpt. Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain, E-mail: Jaime.Haro@upc.es
Recibido el 12 de febrero de 2003; ]]> Aceptado el 23 de septiembre de 2003.
Resumen
En este trabajo estudiamos el número de pares creados en un campo eléctrico usando la aproximación semiclásica. Veremos que en la aproximación semiclásica el proceso estocástico N(t)= "número de pares creados en el instante t", es un proceso estocástico de Poisson con esperanza (αε(t))/(64mc2), donde α es la constante de estructura fina y ε(t) es la energía del campo eléctrico en el instante t.
Descriptores: Producción de pares; comportamiento asintótico de la teoría de perturbaciones; aproximación semiclásica.
Abstract
In this work we study the number of produced pairs in an electric field using the semiclassical aproach. We see that the stochastic process N(t)="net number of produced pairs at time t", is an stochastic Poisson process with expected value (αε (t))/(64mc2), where α is the fine structure constant and ε (t) is the energy of the electric field at time t.
Keywords: Pair production; large-order behaviour of perturbation theory; semiclassical aproach.
]]> PACS: 02.30.Mv; 03.65.Sq; 11.15.Bt; 12.20.Ds
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Referencias
*. Partially supported by DGESIC (Spain), project PB98-0932-C02-01.
1. J.D. Bjorken and S.D. Drell, Relativistic Quantum Fields, (McGraw-Hill Book Co., New York, 1965). [ Links ]
2. R.E. Borcherds and A. Barnard, Quantum Fields Theory, (Notes takes from a course of R.E. Borcherds, Berkeley, 2001). [ Links ]
]]>3. P.A.M. Dirac, The principles of quantum mechanics, (Oxford University Press, 1958). [ Links ]
4. J.M. Eisenberg, G. Kalbermann, Physical Review D 35 (1988) 368. [ Links ]
5. R.P. Feynman, Quantum electrodynamics, (Frontiers in Physics, 1961). [ Links ]
6. R.P. Feynman, S. Weinberg, Elementary particles and the Laws of Physics, (Cambirdge University Press, 1987). [ Links ]
7. W. Greiner, B. Müller, J. Rafelski, Quantum Electrodynamics of Strong Fields, (Springer-Verlang, 1985). [ Links ]
]]>8. E.K.U. Gross, E. Runge, O. Heinonen, Many-Particle Theory, (IOP Pubishing, 1991). [ Links ]
9. G.A. Hagedorn, Comm. Math. Phys. 71 (1980) 77. [ Links ]
10. J. Haro, El límit clàssic de la meccànica quàntica, (Tesi Doctoral, U.A.B. 1997). [ Links ]
11. J. Harthong, ''Etudes sur la mécanique quantique", Asterisque 111 (1984). [ Links ]
12. B.R. Holstein, Am. J. Phys. 67 (1999) 499. [ Links ]
]]>13. C. Itzykson, J.B. Zuber, Quantum field theory, (McGraw-Hill International Editions, 1980). [ Links ]
14. J.C. Le Gillou and J. Zinn-Justin, Large-Order Behaviour of Perturbation Theory, (Current Physics-Sources and Comments, 1990). [ Links ]
15. S.M. Marinov, V.S. Popov, Fortschritte der Physik 25 (1977) 375. [ Links ]
16. V.P. Maslov and M.V. Fedoriuk, Semi-classical aproximation in quantum mechanics, (D.Riedel Publishing Compay, Dordrecht, Holland 1981). [ Links ]
17. A.I. Nikishov, Nuclear Physics B 21 (1970) 346. [ Links ]
]]>18. V.S. Popov, Sov. Phys. JETP 34 (1972) 709. [ Links ]
19. J.S. Schwinger, Physical Review 82 (1951) 664. [ Links ]
20. J.S. Schwinger, Particles, Sources and Fields, (Addison-Wesley Series in Physics, 1970). [ Links ]
21. R. Ticciati, Quantum field theory for mathematicians, (Encyclopedia of mathematics and its applications 72, Cambridge University Press, 1999). [ Links ]
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