Framework of Penrose Transforms on DP-Modules to the Electromagnetic Carpet of the Space-Time from the Moduli Stacks Perspective

DOI: 10.4236/jamp.2014.25019   PDF   HTML     4,608 Downloads   5,360 Views   Citations

Abstract

Considering the different versions of the Penrose transform on D-modules and their applications to different levels of DM-modules in coherent sheaves, we obtain a geometrical re-construction of the electrodynamical carpet of the space-time, which is a direct consequence of the equivalence between the moduli spaces, that have been demonstrated in a before work. In this case, the equivalence is given by the Penrose transform on the quasi coherent Dλ-modules given by the generalized Verma modules diagram established in the Recillas conjecture to the group SO(1, n + 1), and consigned in the Dp-modules on which have been obtained solutions in field theory of electromagnetic type.

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Bulnes, F. (2014) Framework of Penrose Transforms on DP-Modules to the Electromagnetic Carpet of the Space-Time from the Moduli Stacks Perspective. Journal of Applied Mathematics and Physics, 2, 150-162. doi: 10.4236/jamp.2014.25019.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Baston, R.J. and Eastwood, M.G. (1989) The Penrose Transform. The Clarendon Press, Oxford University Press, New York. http://dx.doi.org/10.1007/BF01942327
[2] Eastwood, M.G., Penrose, R. and Wells, R.O. (1981) Cohomology and Massless Fields. Communications in Mathematical Physics, 78, 305-351.
[3] Penrose, R. (1969) Solutions of the Zero-Rest-Mass Equations. Journal of Mathematical Physics, 10, 38-39. http://dx.doi.org/10.1063/1.1664756
[4] Bailey, T.N. and Eastwood, M.G. (1991) Complex Para-Conformal Manifolds Their Differential Geometry and Twistor Theory. Forum Mathematicum, 3, 61-103. http://dx.doi.org/10.1515/form.1991.3.61
[5] Bulnes, F. (2013) Penrose Transform on Induced DG/H-Modules and Their Moduli Stacks in the Field Theory. Advances in Pure Mathematics, 3, 246-253.
[6] D’Agnolo, A. and Shapira, P. (1996) Radon-Penrose Transform for D-Modules. Journal of Functional Analysis, 139, 349-382. http://dx.doi.org/10.1006/jfan.1996.0089
[7] Kapustin, A., Kreuser, M. and Schlesinger, K.G. (2009) Homological Mirror Symmetry: New Developments and Perspectives. Springer. Berlin, Heidelberg.
[8] Bulnes, F. (2013) Geometrical Langlands Ramifications and Differential Operators Classification by Coherent D-Modules in Field Theory. Journal of Mathematics and System Sciences, 3, 491-507.
[9] Kashiwara, M. (1989) Representation Theory and D-Modules on Flag Varieties. Astérisque, 173-174, 55-109.
[10] Helgason, S. (1999) The Radon Transform. Birkhauser Boston, Mass. http://dx.doi.org/10.1007/978-1-4757-1463-0
[11] Marastoni, C. and Tanisaki, T. (2003) Radon Transforms for Quasi-Equivariant D-Modules on Generalized Flag Manifolds. Differential Geometry and its Applications, 18, 147-176. http://dx.doi.org/10.1016/S0926-2245(02)00145-6
[12] Mason, L. and Skinner, D. (2007) Heterotic Twistor-String Theory. Oxford University.
[13] Gindikin, S. Penrose Transform at Flag Domains. The Erwin Schrödinger International Institute for Mathematical Physics. Boltzmanngasse 9, A-1090, Wien Austria.
[14] Bulnes, F. (2011) Cohomology of Moduli Spaces in Differential Operators Classification to the Field Theory (II). Proceedings of FSDONA-11 (Function Spaces, Differential Operators and Non-linear Analysis), Tabarz Thur, Germany, 1, 001-022.
[15] Kashiwara, M. and Schmid, W. (1994) Quasi-Equivariant D-Modules, Equivariant Derived Category, and Representations of Reductive Lie Groups, in Lie Theory and Geometry. Progr. Math., Birkhäuser, Boston, 123, 457-488.
[16] Bulnes, F. (2012) Penrose Transform on D-Modules, Moduli Spaces and Field Theory. Advances in Pure Mathematics, 2, 379-390. http://dx.doi.org/10.4236/apm.2012.26057
[17] Bulnes, F. (2013) Orbital Integrals on Reductive Lie Groups and Their Algebras. Intech, Rijeka, Croatia. http://www.intechopen.com/books/orbital-integrals-on-reductive-lie-groups-and-their-algebras/orbital-integrals-on-reductive-lie-groups-and-their-algebrasB
[18] Ratcliffe, J.G. (2006) Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics. 2nd Edition, 149, Springer-Verlag, Berlin, New York.
[19] Bulnes, F. (2009) Design of Measurement and Detection Devices of Curvature through of the Synergic Integral Operators of the Mechanics on Light Waves. ASME, Internal. Proc. Of IMECE, Florida, 91-102.
[20] Antoine, J.P. and Jacques, M. (1984) Class. Quantum Grav., 1, 431. http://dx.doi.org/10.1088/0264-9381/1/5/002
[21] Dunne, E.G. and Eastwood, M. (1990) The Twistor Transform. In: Bailey, T.N. and Baston, R.J., Eds., Twistor in Mathematics and Physics, Cambridge University Press, 110-127.
[22] Bulnes, F. (2006) Doctoral Course of Mathematical Electrodynamics. Internal. Proc. Appliedmath, 2, 398-447.
[23] Benzvi, D. and Nadler, D. (2011) The Character Theory of Complex Group.
[24] Mebkhout, Z. (1977) Local Cohomology of Analytic Spaces. Rubl. RIMS, Kioto, Univ., 12, 247-256.
[25] Hausel, T. and Thaddeus, M. (2003) Mirror Symmetry, Langlands Duality and the Hitchin System. Inventiones Mathematicae., 153, 197-229. http://dx.doi.org/10.1007/s00222-003-0286-7
[26] Bershadsky, M., Johansen, A., Sadov, V. and Vafa, C. (1995) Topological Reduction of 4-d SYM to 2-d Sigma Models. Nuclear Physics B, 448, 166. http://dx.doi.org/10.1016/0550-3213(95)00242-K
[27] Weylman, H. (2012) Path Integrals for Photons: The Framework for the Electrodynamics Carpet of the Space-Time. Journal on Photonics and Spintronics, 1, 21-27.
[28] Bulnes, F. (2012) Electromagnetic Gauges and Maxwell Lagrangians Applied to the Determination of Curvature in the Space-Time and their Applications. Journal of Electromagnetic Analysis and Applications, 4, 252-266. http://dx.doi.org/10.4236/jemaa.2012.46035

  
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