Skip to main content
Log in

Dirichlet boundary conditions in a noncommutative theory

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We study the problem of imposing Dirichlet-like boundary conditions along a static spatial curve, in a planar Noncommutative Quantum Field Theory model.

After constructing interaction terms that impose the boundary conditions, we discuss their implementation at the level of an interacting theory, with a focus on their physical consequences, and the symmetries they preserve. We also derive the effect they have on certain observables, like the Casimir energies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Bordag, U. Mohideen and V.M. Mostepanenko, New developments in the Casimir effect, Phys. Rept. 353 (2001) 1 [quant-ph/0106045] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. K.A. Milton, The Casimir effect: physical manifestations of the zero-point energy, World Scientific, Singapore (2001).

    Book  MATH  Google Scholar 

  3. S. Reynaud et al., Quantum vacuum fluctuations, C.R. Acad. Sci. Paris 2-IV (2001) 1287 [quant-ph/0105053] [SPIRES].

    Google Scholar 

  4. K.A. Milton, The Casimir effect: Recent controversies and progress, J. Phys. A 37 (2004) R209 [hep-th/0406024] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  5. S.K. Lamoreaux, The Casimir force: background, experiments, and applications, Rep. Prog. Phys. 68 (2005) 201.

    Article  ADS  Google Scholar 

  6. M. Bordag, G.L. Klimchitskaya, U. Mohideen and V.M. Mostepanenko, Advances in the Casimir effect, Oxford University Press, Oxford U.K. (2009).

    Book  MATH  Google Scholar 

  7. M.R. Douglas and N.A. Nekrasov, Noncommutative field theory, Rev. Mod. Phys. 73 (2001) 977 [hep-th/0106048] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. R. Casadio, A. Gruppuso, B. Harms and O. Micu, Boundaries and the Casimir effect in non-commutative space-time, Phys. Rev. D 76 (2007) 025016 [arXiv:0704.2251] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  9. C.D. Fosco and G.A. Moreno, Casimir effect in 2 + 1 dimensional noncommutative theories, Phys. Lett. B 659 (2008) 901 [arXiv:0711.4272] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  10. G.V. Dunne and R. Jackiw, ‘Peierls substitution’ and Chern-Simons quantum mechanics, Nucl. Phys. Proc. Suppl. 33C (1993) 114 [hep-th/9204057] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. C.D. Fosco and A. López, Aspects of noncommutative descriptions of planar systems in high magnetic fields, J. Phys. A 37 (2004) 4123.

    ADS  Google Scholar 

  12. L. Susskind, The quantum Hall fluid and non-commutative Chern Simons theory, hep-th/0101029 [SPIRES].

  13. R. Jackiw, V.P. Nair, S.Y. Pi and A.P. Polychronakos, Perfect fluid theory and its extensions, J. Phys. A 37 (2004) R327.

    ADS  Google Scholar 

  14. L. Mezincescu, Star operation in quantum mechanics, hep-th/0007046 [SPIRES].

  15. C.D. Fosco, F.C. Lombardo and F.D. Mazzitelli, Neumann Casimir effect: a singular boundary-interaction approach, Phys. Lett. B 690 (2010) 189 [arXiv:0912.0886] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  16. E. Langmann and R.J. Szabo, Duality in scalar field theory on noncommutative phase spaces, Phys. Lett. B 533 (2002) 168 [hep-th/0202039] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  17. H. Grosse and R. Wulkenhaar, Renormalisation of phi**4 theory on noncommutative R 2 in the matrix base, JHEP 12 (2003) 019 [hep-th/0307017] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. C.D. Fosco and G.A. Moreno, One-loop effects in a self-dual planar noncommutative theory, JHEP 11 (2007) 046 [arXiv:0710.0818] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. R. Gopakumar, S. Minwalla and A. Strominger, Noncommutative solitons, JHEP 05 (2000) 020 [hep-th/0003160] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. N. Nekrasov and A.S. Schwarz, Instantons on noncommutative R 4 and (2, 0) superconformal six dimensional theory, Commun. Math. Phys. 198 (1998) 689 [hep-th/9802068] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. A.A. Bichl, A note on UV/IR mixing and non-commutative instanton calculus, hep-th/0312230 [SPIRES].

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to C. D. Fosco.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fosco, C.D., Scuracchio, P. Dirichlet boundary conditions in a noncommutative theory. J. High Energ. Phys. 2010, 66 (2010). https://doi.org/10.1007/JHEP09(2010)066

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP09(2010)066

Keywords

Navigation