HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 126 (2011) > Number 3
| Next Article >

Prog. Theor. Phys. Vol. 126 No. 3 (2011) pp. 419-434

[ Full Text PDF : FREE ACCESS (219K) ]

Local Zeta Regularization and the Casimir Effect

Davide Fermi1,* and Livio Pizzocchero2,3,**

1Università di Milano
2Dipartimento di Matematica, Università di Milano, Via C. Saldini 50, I-20133 Milano, Italy
3Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Italy

(Received June 14, 2011; Revised July 15, 2011)

Abstract:

The local zeta regularization allows to treat local divergences appearing in quantum field theory; these are renormalized by pure analytic continuation (in the parameter of the regulator), with no need to remove or subtract divergent terms. This approach can be applied to the stress-energy tensor of the Casimir effect, and works as well on curved space-times.
It is not useless to illustrate the power and elegance of this method in a simple case. In the present paper, our attention is devoted to the case of a neutral, massless scalar field in flat space-time, on a space domain with suitable (e.g., Dirichlet) boundary conditions. After a general outline of the local zeta method for the Casimir effect, we exemplify it in the typical case of a (Dirichlet) field between two parallel plates, or outside them. The results agree with the ones obtained by more popular methods, such as point splitting regularization. Connections with the existing literature on this subject are indicated.

Subject Index : 130, 132, 187
URL : http://ptp.ipap.jp/link?PTP/126/419/
DOI : 10.1143/PTP.126.419


*E-mail: davide.fermi@studenti.unimi.it
**E-mail: livio.pizzocchero@unimi.it

[ Full Text PDF : FREE ACCESS (219K) ] Citation:

References:

  1. S. K. Blau, M. Visser and A. Wipf, Nucl. Phys. B 310 (1988), 163[CrossRef].
  2. E. Elizalde, S. D. Odintsov, A. Romeo, A. A. Bytsenko and S. Zerbini, Zeta regularization techniques with applications (World Scientific, Singapore, 1994).
  3. S. W. Hawking, Commun. Math. Phys. 55 (1977), 133[CrossRef].
  4. R. M. Wald, Commun. Math. Phys. 70 (1979), 221[CrossRef].
  5. V. Moretti, Phys. Rev. D 56 (1997), 7797[APS].
  6. D. Iellici and V. Moretti, Phys. Lett. B 425 (1998), 33[CrossRef].
  7. V. Moretti, Commun. Math. Phys. 201 (1999), 327[CrossRef].
  8. A. A. Bytsenko, G. Cognola, E. Elizalde, V. Moretti and S. Zerbini, Analytic aspects of quantum fields (World Scientific, 2003).
  9. D. Deutsch and P. Candelas, Phys. Rev. D 20 (1979), 3063[APS].
  10. S. A. Fulling, Aspects of quantum field theory in curved space time (Cambridge University Press, 1989).
  11. K. A. Milton, The Casimir effect - Physical manifestations of zero-point energy (World Scientific, 2001).
  12. G. Esposito, G. M. Napolitano and L. Rosa, Phys. Rev. D 77 (2008), 105011, [APS] arXiv:0803.0861v1[e-print arXiv].
  13. J. Schwinger, Particles, sources, and fields (Perseus Books, Reading, Massachusets, 1998).
  14. L. E. Parker and D. J. Toms, Quantum field theory in curved spacetime (Cambridge University Press, 2009).
  15. L. S. Brown and G. J. Maclay, Phys. Rev. 184 (1969), 1272[APS].
  16. S. M. Christensen, Phys. Rev. D 14 (1976), 2490[APS].
  17. F. W. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark, NIST Handbook of mathematical functions (Cambridge University Press, 2010).
  18. A. Jonquière, Bull. Soc. Math. France 17 (1889), 142, available at http://www.numdam.org/
  19. A. Romeo and A. A. Saharian, J. of Phys. A 35 (2002), 1297[CrossRef].

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.