Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2017, Article ID 6124189, 11 pages
https://doi.org/10.1155/2017/6124189
Research Article

Double Hodge Theory for a Particle on Torus

Department of Physics, Banaras Hindu University, Varanasi 221005, India

Correspondence should be addressed to Vipul Kumar Pandey; moc.liamg@isanaravlupiv

Received 1 July 2017; Accepted 31 October 2017; Published 27 November 2017

Academic Editor: Edward Sarkisyan-Grinbaum

Copyright © 2017 Vipul Kumar Pandey and Bhabani Prasad Mandal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. C. Becchi, A. Rouet, and R. Stora, “The abelian Higgs Kibble model, unitarity of the S-operator,” Physics Letters B, vol. 52, no. 3, pp. 344–346, 1974. View at Publisher · View at Google Scholar · View at Scopus
  2. C. Becchi, A. Rouet, and R. Stora, “Renormalization of gauge theories,” Annals of Physics, vol. 98, no. 2, pp. 287–321, 1976. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. I. V. Tyutin, “Gauge invariance in field theory and statistical physics in operator formalism,” Lebedev Report N Fian, vol. 39, 1975. View at Google Scholar
  4. M. Chaichian and N. F. Nelipa, Introduction to gauge field theories, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1984.
  5. J. Polchinski, Superstring Theory and Beyond String Theory, vol. 2 of Cambridge, UK, Cambridge University Press, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  6. E. Witten, “On background-independent open-string field theory,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 46, no. 12, pp. 5467–5473, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. K. Hotta, “Finite temperature systems of brane-antibrane on a torus,” Journal of High Energy Physics, vol. 0309, p. 002, 2003. View at Publisher · View at Google Scholar
  8. J. J. Atick and E. Witten, “The Hagedorn transition and the number of degrees of freedom of string theory,” Nuclear Physics B, vol. 310, no. 2, pp. 291–334, 1988. View at Publisher · View at Google Scholar · View at Scopus
  9. S. S. Gubser, S. Gukov, I. R. Klebanov, M. Rangamani, and E. Witten, “The Hagedorn transition in noncommutative open string theory,” Journal of Mathematical Physics, vol. 42, no. 7, pp. 2749–2764, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. M. Aguado, M. Asorey, and A. Wipf, “Nahm transform and moduli spaces of N-models on the torus,” Annals of Physics, vol. 298, no. 1, pp. 2–23, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  11. K.-L. Chan and M. Cvetic, “Massless BPS-saturated states on the two-torus moduli sub-space of heterotic string,” Physics Letters. B. Particle Physics, Nuclear Physics and Cosmology, vol. 375, no. 1-4, pp. 98–102, 1996. View at Google Scholar · View at MathSciNet
  12. S.-T. Hong, “BRST symmetric in free particle system on toric geometry,” Modern Physics Letters A, vol. 20, no. 21, pp. 1577–1588, 2005. View at Google Scholar · View at MathSciNet
  13. M. Lavelle and D. McMullan, “Nonlocal symmetry for QED,” Physical Review Letters, vol. 71, no. 23, pp. 3758–3761, 1993. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Tang and D. Finkelstein, “Relativistically covariant symmetry in QED,” Physical Review Letters, vol. 73, no. 23, pp. 3055–3057, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. Lavelle and D. McMullan, “Lavelle and McMullan reply 1,” Physical Review Letters, vol. 75, no. 22, p. 4151, 1995. View at Publisher · View at Google Scholar · View at Scopus
  16. P. Bracken, “The Hodge-de Rham decomposition theorem and an application to a partial differential equation,” Acta Mathematica Hungarica, vol. 133, no. 4, pp. 332–341, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. S. I. Goldberg, Curvature and Homology, Dover Publications, Inc., Mineola, NY, USA, 1970.
  18. S. Morita, Geometry of Differential Forms, vol. 209 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, 2001. View at MathSciNet
  19. F. W. Warner, Foundations of differentiable manifolds and Lie groups, vol. 94 of Graduate Texts in Mathematics, Springer-Verlag, New York-Berlin, 1983. View at MathSciNet
  20. T. Eguchi, P. B. Gilkey, and A. J. Hanson, “Gravitation, gauge theories and differential geometry,” Physics Reports, vol. 66, no. 6, pp. 213–393, 1980. View at Publisher · View at Google Scholar · View at MathSciNet
  21. K. Nishijima, “The Casimir operator in the representations of BRS algebra,” Progress of Theoretical and Experimental Physics, vol. 80, no. 5, pp. 897–904, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  22. K. Nishijima, “Observable states in the representations of BRS algebra,” Progress of Theoretical and Experimental Physics, vol. 80, no. 5, pp. 905–912, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  23. W. Kalau and J. W. van Holten, “BRST cohomology and BRST gauge fixing,” Nuclear Physics B, vol. 361, no. 1, pp. 233–252, 1991. View at Publisher · View at Google Scholar · View at Scopus
  24. J. W. van Holten, “Becchi-Rouet-Stora-Tyutin cohomology of compact gauge algebras,” Physical Review Letters, vol. 64, no. 24, pp. 2863–2865, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  25. J. W. van Holten, “The BRST complex and the cohomology of compact lie algebras,” Nuclear Physics B, vol. 339, no. 1, pp. 158–176, 1990. View at Publisher · View at Google Scholar · View at Scopus
  26. H. Aratyn, “BRS cohomology in string theory: geometry of abelization and the quartet mechanism,” Journal of Mathematical Physics, vol. 31, no. 5, article 1240, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. E. Harikumar, R. P. Malik, and M. Sivakumar, “Hodge decomposition theorem for abelian two-form gauge theory,” Journal of Physics A: Mathematical and General, vol. 33, no. 40, pp. 7149–7163, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  28. J. Wess and B. Zumino, “Consequences of anomalous ward identities,” Physics Letters B, vol. 37, no. 1, pp. 95–97, 1971. View at Publisher · View at Google Scholar · View at Scopus
  29. S. D. Joglekar and B. P. Mandal, “Finite field-dependent BRS transformations,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 51, no. 4, pp. 1919–1928, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  30. S. D. Joglekar and A. Misra, “Relating Green's functions in axial and Lorentz gauges using finite field-dependent BRS transformations,” Journal of Mathematical Physics, vol. 41, no. 4, pp. 1755–1767, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  31. M. Plyushchay, “Hidden nonlinear supersymmetries in pure parabosonic systems,” International Journal of Modern Physics A, vol. 15, no. 23, pp. 3679–3698, 2000. View at Publisher · View at Google Scholar
  32. S. D. Joglekar and A. Misra, “A Derivation of the Correct Treatment of Singularities in Axial Gauges,” Modern Physics Letters A, vol. 14, no. 30, pp. 2083–2092, 1999. View at Publisher · View at Google Scholar
  33. S. D. Joglekar and A. Misra, “Wilson loop and the treatment of axial gauge poles,” Modern Physics Letters A, vol. 15, no. 08, pp. 541–546, 2000. View at Publisher · View at Google Scholar
  34. S. D. Joglekar, “Green's functions in axial- and lorentz-type gauges and brs transformations,” Modern Physics Letters A, vol. 15, no. 04, pp. 245–252, 2000. View at Publisher · View at Google Scholar
  35. S. D. Joglekar and B. P. Mandal, “Application of finite field-dependent BRS transformations to problems of the Coulomb gauge,” International Journal of Modern Physics A, vol. 17, pp. 1279–1300, 2002. View at Google Scholar
  36. S. D. Joglekar and J. Mod, “Connecting Green's Functions in an Arbitrary Pair of Gauges and an Application to Planar Gauges Satish D. Joglekar,” International Journal of Modern Physics A, vol. 16, pp. 5043–5060, 2001. View at Google Scholar
  37. R. Banerjee and B. P. Mandal, “Quantum gauge symmetry from finite field dependent BRST transformations,” Physics Letters. B. Particle Physics, Nuclear Physics and Cosmology, vol. 488, no. 1, pp. 27–30, 2000. View at Google Scholar · View at MathSciNet
  38. R. S. Bandhu and S. D. Joglekar, “Finite field-dependent BRS transformation and axial gauges,” Journal of Physics A: Mathematical and General, vol. 31, no. 18, pp. 4217–4224, 1998. View at Publisher · View at Google Scholar · View at Scopus
  39. S. Upadhyay and B. P. Mandal, “Relating Gribov-Zwanziger theory to effective Yang-Mills theory,” EPL (Europhysics Letters), vol. 93, no. 3, Article ID 31001, 2011. View at Publisher · View at Google Scholar · View at Scopus
  40. S. Deguchi, V. K. Pandey, and B. P. Mandal, “Maximal Abelian gauge and a generalized BRST transformation,” Physics Letters B, vol. 756, pp. 394–399, 2016. View at Publisher · View at Google Scholar · View at Scopus
  41. S. Upadhyay and B. P. Mandal, “Generalized BRST symmetry for arbitrary spin conformal field theory,” Physics Letters. B. Particle Physics, Nuclear Physics and Cosmology, vol. 744, pp. 231–236, 2015. View at Google Scholar · View at MathSciNet
  42. S. Upadhyay, A. Reshetnyak, and B. P. Mandal, “Comments on interactions in the SUSY models,” The European Physical Journal C, vol. 76, no. 7, article no. 391, 2016. View at Publisher · View at Google Scholar · View at Scopus
  43. M. Faizal, S. Upadhyay, and B. P. Mandal, “Finite field-dependent BRST symmetry for ABJM theory in N=1 superspace,” Physics Letters B, vol. 738, pp. 201–205, 2014. View at Publisher · View at Google Scholar · View at Scopus
  44. P. A. M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science, Yeshiva University Press, New York, NY, USA, 1964. View at MathSciNet
  45. M. Henneaux, “Hamiltonian form of the path integral for theories with a gauge freedom,” Physics Reports, vol. 126, no. 1, pp. 1–66, 1985. View at Google Scholar · View at MathSciNet
  46. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, Princeton University Press, 1992. View at MathSciNet
  47. K. Sundermeyer, Constrained Dynamics, vol. 169 of Lecture Notes in Physics, Springer, Berlin, Germany, 1982. View at MathSciNet
  48. I. A. Batalin and E. S. Fradkin, “A generalized canonical formalism and quantization of reducible gauge theories,” Physics Letters B, vol. 122, no. 2, pp. 157–164, 1983. View at Publisher · View at Google Scholar · View at Scopus
  49. E. S. Fradkin and G. A. Vilkovisky, “Quantization of relativistic systems with constraints,” Physics Letters B, vol. 55, no. 2, pp. 224–226, 1975. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  50. S. Upadhyay and B. P. Mandal, “The model for self-dual chiral bosons as a Hodge theory,” The European Physical Journal C, vol. 71, no. 9, article 1759, 2011. View at Publisher · View at Google Scholar · View at Scopus
  51. S. Upadhyay and B. P. Mandal, “Noncommutative gauge theories: model for Hodge theory,” International Journal of Modern Physics A, vol. 28, no. 25, 1350122, 15 pages, 2013. View at Google Scholar · View at MathSciNet
  52. S. Upadyay, “Quantum gauge symmetry from finite field dependent BRST transformations,” High Energy Physics - Theory, 2013. View at Publisher · View at Google Scholar
  53. S. K. Rai and B. P. Mandal, “Finite nilpotent BRST transformations in Hamiltonian formulation,” International Journal of Theoretical Physics, vol. 52, no. 10, pp. 3512–3521, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  54. R. Kumar, “Off-shell nilpotent (anti-)BRST symmetries for a free particle system on a toric geometry: superfield formalism,” EPL (Europhysics Letters), 106, 51001, 2014.