Biblioteca de la Universidad Complutense de Madrid

Divergence of perturbation theory: Steps towards a convergent series

Impacto

Oleaga Apadula, Gerardo Enrique y Pernice, Sergio A. (1998) Divergence of perturbation theory: Steps towards a convergent series. Physical Review D , 57 (2). 1144-1158 . ISSN 1550-7998

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.

290kB

URL Oficial: http://prd.aps.org/pdf/PRD/v57/i2/p1144_1




Resumen

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of Lebesgue's dominated convergence theorem using familiar techniques of quantum held theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.


Tipo de documento:Artículo
Palabras clave:Optimized delta-expansion; Connected vacuum amplitude; Order dependent mappings; Quantum-field theory; Anharmonic-oscillator; Variational calculation; Nonlinear-systems; Zero dimensions; Proof; Approximations
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:17294
Referencias:

F. J. Dyson, Phys. Rev. 85, 631 (1951) .

Large-Order Behaviour of Perturbation Theory, edited by J. C. Le Guillou and J. Zinn-Justin North-Holland, Amsterdam, 1990).

C. M. Bender and T. T. Wu, Phys. Rev. D 7, 1620 (1973) .

C. M. Bender and T. T. Wu, Phys. Rev. 148, 1231 (1969).

B. Simon, in Cargese Lectures in Physics, edited by D. Bessis (Gordon and Beach, New York, 1972), Vol. 5

J. J. Loeffel et al., Phys. Lett. 30B, 1656 (1968)

ibid.S. Graffi et al., 32B, 631 (1970)

B. Simon, Functional Integration and Quantum Physics (Academic Press, New York, 1979).

See, for example, G. ’t Hooft, in Erice Lectures 1977, edited by A. Zichichi (Plenum, New York, 1979).

G. Hardy, Divergent Series (Oxford University Press, New York, 1949);E. Borel, Lecons sur les series divergent (1922).

J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 2nd ed. (Clarendon, Oxford, 1993).

A. Duncan and H. F. Jones, Phys. Rev. D 47, 2560 (1993) .

C. M. Bender, A. Duncan, and H. F. Jones, Phys. Rev. D 49, 4219 (1994).

H. Kleinert, Phys. Lett. A 173, 332 (1993)

ibid.J. Jaenicke and H. Kleinert, 176, 409 (1993)

ibid.H. Kleinert and H. Meyer, 184, 319 (1994)

W. Janke and H. Kleinert, 199, 287 (1995)

W. Janke and H. Kleinert, quant-ph/9502019.

C. Arvanitis, H. F. Jones, and C. S. Parker, Phys. Rev. D 52, 3704 (1995) .

R. Guida, K. Konishi, and H. Suzuki, Ann. Phys. (N.Y.) 241, 152 (1995) .

R. Guida, K. Konishi, and H. Suzuki, Ann. Phys. (N.Y.) 249, 109 (1996) .

B. Bellet, P. Garcia, A. Neveu, Int. J. Mod. Phys. A 11, 5587 (1996)

C. Arvanitis, F. Geniet, and A. Neveu, PM-94-19, hep-th/9506188

C. Arvanitis, F. Geniet, M. Iacomi, J. L. Kneur, and A. Neveu, Int. J. Mod. Phys. A 12, 3307 (1997) .

J. Glimm and A. Jaffe, Quantum Physics, A Functional Integral Point of View, 2nd ed. (Springer-Verlag, Berlin, 1987).

G. H. Derrick, J. Math. Phys. 5, 1252 (1964) .

G. Auberson et al., Nuovo Cimento A 48, 1 (1978).

W. E. Caswell, Ann. Phys. (N.Y.) 123, 153 (1979)

I. G. Halliday and P. Suranyi, Phys. Lett. 85B, 421 (1979); Phys. Rev. D 21, 1529 (1981)

J. Killingbeck, J. Phys. A 14, 1005 (1981)

B. S. Shaverdyan and A. G. Ushveridze, Phys. Lett. 123B, 316 (1983)

R. P. Feynman and H. Kleinert, Phys. Rev. A 34, 5080 (1986)

R. Giachetti and V. Tognetti, Phys. Rev. Lett. 55, 912 (1985) ; Int. J. Magn. Magn. Mater. 54-57, 861 (1986)

R. Giachetti, V. Tognetti, and R. Vaia, Phys. Rev. B 33, 7647 (1986)

A. Okopinska, Phys. Rev. D 35, 1835 (1987)

A. Duncan and M. Moshe, Phys. Lett. B 215, 352 (1988)

C. M. Bender et al., Phys. Rev. D 37, 1472 (1988)

A. Duncan and H. F. Jones, Nucl. Phys. B320, 189 (1989)

H. F. Jones and M. Moshe, Phys. Lett. B 234, 492 (1990)

I. Stancu and P. M. Stevenson, Phys. Rev. D 42, 2710 (1990)

V. I. Yukalov, J. Math. Phys. 32, 1235 (1991)

A. Neveu, Festschrift for A. Martin (Springer, Berlin, 1991)

S. K. Gandhi et al., Nucl. Phys. B359, 429 (1991)

A. N. Sissakian and I. L. Solovtsov, Z. Phys. C 54, 263(1992) .

P. M. Stevenson, Phys. Rev. D 23, 2916 (1981) .

I. R. C. Buckley, A. Duncan, and H. F. Jones, Phys. Rev. D 47, 2554 (1993) .

R. Seznec and J. Zinn-Justin, J. Math. Phys. 20, 1398 (1979) .

Le Guillou and J. Zinn-Justin, Ann. Phys. (N.Y.) 147, 57 (1983).

Depositado:03 Dic 2012 10:38
Última Modificación:07 Feb 2014 09:45

Sólo personal del repositorio: página de control del artículo