Integral Geometry and Complex Space-Time Cohomology in Field Theory
Pure and Applied Mathematics Journal
Volume 3, Issue 6-2, December 2014, Pages: 30-37
Received: Dec. 4, 2014; Accepted: Dec. 6, 2014; Published: Dec. 27, 2014
Views 3219      Downloads 178
Francisco Bulnes, Head of Research Department in Mathematics and Engineering, TESCHA, Chalco, Mexico
Ronin Goborov, Department of Mathematics, Lomonosov University, Moscu, Russia
Article Tools
Follow on us
Through of a cohomological theory based in the relations between integrating invariants and their different differential operators classes in the field equations as well as of functions inside of the integral geometry are established equivalences among cycles and co-cycles of the closed sub-manifolds, line bundles and contours of the space-time modeled as complex Riemannian manifold obtaining a cohomology of general integrals useful in the evaluation and measurement of fields, particles and physical interactions of diverse nature in field theory. Also are used embeddings of cycles in the complex Riemannian manifold through of the dualities: line bundles with cohomological contours and closed sub-manifolds with cohomological functional to build cohomological spaces of integrals as solution classes of the corresponding field equations.
Complex Cohomology, Cohomology of Cycles, Cohomological Functional, Integral Operator Cohomology, Integrating Invariants, Integral Topology, Cohomological Classes
To cite this article
Francisco Bulnes, Ronin Goborov, Integral Geometry and Complex Space-Time Cohomology in Field Theory, Pure and Applied Mathematics Journal. Special Issue: Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program. Vol. 3, No. 6-2, 2014, pp. 30-37. doi: 10.11648/j.pamj.s.2014030602.16
F. Bulnes, “Radon Transform, Generalizations and Penrose Transform,” Proc. 4th Appliedmath, Special Section in Functional Analysis and Differential Equations, Mexico, 2009, pp63-76.
F. Bulnes, M. Shapiro, On general theory of integral operators to analysis and geometry, IM-UNAM, SEPI-IPN, Monograph in Mathematics, 1st ed., J. P. Cladwell, Ed. Mexico: 2007.
F. Bulnes, “Integral Theory of the Universe,” Internal. Proc. 2nd Appliedmath, IM-UNAM, SEPI-IPN, Mexico, 2006, pp73-121.
F. Bulnes, “Doctoral Course of Mathematical Electrodynamics,” Internal. Proc. 2nd Appliedmath: Conferences and Advances Courses, IM-UNAM, SEPI-IPN, Mexico, 2006, pp398-447.
F. Bulnes, “On the Last Progress of Cohomological Induction in the Problem of Classification of Lie Groups Representations,” Internal. Conf. of Infinite Dimensional Analysis and Topology, Book of Plenary Conferences, Precarpathian National University, Ukraine, 2009.
F. Bulnes, Conferences of Lie groups (representation theory of reductive Lie groups), Monograph in Pure Mathematics, IM-UNAM, SEPI-IPN, 2nd Ed., Paul Cladwell, Mexico, 2005.
H. Bateman, “The Solution of Partial Differential Equations by Means of Definite Integrals,” Proc. Lon. Math. Soc. 1 (2) (1904) 451-458.
R. J. Baston, “Local Cohomology Elementary States and Evaluation Twistor,” Newsletter (Oxford Preprint) 22 8-13, 1986.
R. Baston, M. Eastwood, “The Penrose Transform its Interaction with Representation Theory,” Oxford University Press, 1989.
S. Helgason, The Radon transform, Prog. Math. Vol. 5, Birkhäuser, 1980.
S. Gindikin, “The Penrose Transform and Complex Integral Geometry Problems,” Modern Problems of Mathematics (Moscow), Vol. 17, 1981, pp. 57-112.
S. Gindikin, Between integral geometry and twistors, Twistors in Mthematics and Physics, Cmbridge University Press, 1990.
S. Gindikin, Generalized conformal structures, Twistors in Mthematics and Physics, Cmbridge University Press, 1990.
Z. Mebkhout, Sur le problème de Hilbert–Riemann, Lecture notes in physics 129 (1980) 99–110.
M. Kashiwara, Faisceaux constructibles et systèmes holonomes d'équations aux dérivées partielles linéaires à points singuliers réguliers, Séminaire Goulaouic-Schwartz, 1979–80, exp. 19.
E. Dunne, M. G. Eastwood, A twistor transform for the discrete series: the case of SU(2), Twistor Newsletter, Twistor Newsletter 26 (March 1988), pp26-30.
Y. Stropovsvky, “Functors on ∞- Categories and the Yoneda Embedding,” Pure and Applied Mathematics Journal. Vol. 3, No. 2, 2014, pp. 20-25. doi: 10.11648/j.pamj.s.20140302.14
F. Bulnes, Penrose Transform on Induced DG/H-Modules and Their Moduli Stacks in the Field Theory, Advances in Pure Mathematics 3 (2) (2013) 246-253. doi: 10.4236/apm.2013.32035.
I. M. Gelfand, Generalized functions, Vol. 5. Academic Press, N. Y., 1952.
V. Bargmann, E. P. Wigner, “Group Theoretical Discussion of Relativistic Wave Equations,” PNAS, 34, 1948.
I. Bialynicki-Birula, E. T. Newman, J. Porter, J. Winicour, B. Lukacs, Z. Perjes, A. Sebestyen, “A Note on Helicity,” J. Math. Phys., 22. 1981.
F. Burstall, J. Rawnsley, Twistor theory for Riemannian symmetric space, Springer, 1990.
N. Woodhouse, “Contour Integrals for the Ultrahyperbolic Wave Equation,” Proc. Math. Phys., 438, 1992.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186