Integral Geometry and Complex Space-Time Cohomology in Field Theory

Francisco Bulnes; Ronin Goborov

doi:doi:10.11648/j.pamj.s.2014030602.16

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Integral Geometry and Complex Space-Time Cohomology in Field Theory

Francisco Bulnes, Ronin Goborov

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 6-2)

Received: 4 December 2014 Accepted: 6 December 2014 Published: 27 December 2014

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Abstract

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.

Published in	Pure and Applied Mathematics Journal (Volume 3, Issue 6-2) This article belongs to the Special Issue Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program
DOI	10.11648/j.pamj.s.2014030602.16
Page(s)	30-37
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Complex Cohomology, Cohomology of Cycles, Cohomological Functional, Integral Operator Cohomology, Integrating Invariants, Integral Topology, Cohomological Classes

References

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[2]	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.
[3]	F. Bulnes, “Integral Theory of the Universe,” Internal. Proc. 2nd Appliedmath, IM-UNAM, SEPI-IPN, Mexico, 2006, pp73-121.
[4]	F. Bulnes, “Doctoral Course of Mathematical Electrodynamics,” Internal. Proc. 2nd Appliedmath: Conferences and Advances Courses, IM-UNAM, SEPI-IPN, Mexico, 2006, pp398-447.
[5]	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.
[6]	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.
[7]	H. Bateman, “The Solution of Partial Differential Equations by Means of Definite Integrals,” Proc. Lon. Math. Soc. 1 (2) (1904) 451-458.
[8]	R. J. Baston, “Local Cohomology Elementary States and Evaluation Twistor,” Newsletter (Oxford Preprint) 22 8-13, 1986.
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[10]	S. Helgason, The Radon transform, Prog. Math. Vol. 5, Birkhäuser, 1980.
[11]	S. Gindikin, “The Penrose Transform and Complex Integral Geometry Problems,” Modern Problems of Mathematics (Moscow), Vol. 17, 1981, pp. 57-112.
[12]	S. Gindikin, Between integral geometry and twistors, Twistors in Mthematics and Physics, Cmbridge University Press, 1990.
[13]	S. Gindikin, Generalized conformal structures, Twistors in Mthematics and Physics, Cmbridge University Press, 1990.
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[15]	M. Kashiwara, Faisceaux constructibles et systèmes holonomes d'équations aux dérivées partielles linéaires à points singuliers réguliers, Séminaire Goulaouic-Schwartz, 1979–80, exp. 19.
[16]	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.
[17]	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
[18]	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.
[19]	I. M. Gelfand, Generalized functions, Vol. 5. Academic Press, N. Y., 1952.
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APA Style

Francisco Bulnes, Ronin Goborov. (2014). Integral Geometry and Complex Space-Time Cohomology in Field Theory. Pure and Applied Mathematics Journal, 3(6-2), 30-37. https://doi.org/10.11648/j.pamj.s.2014030602.16

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ACS Style

Francisco Bulnes; Ronin Goborov. Integral Geometry and Complex Space-Time Cohomology in Field Theory. Pure Appl. Math. J. 2014, 3(6-2), 30-37. doi: 10.11648/j.pamj.s.2014030602.16

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AMA Style

Francisco Bulnes, Ronin Goborov. Integral Geometry and Complex Space-Time Cohomology in Field Theory. Pure Appl Math J. 2014;3(6-2):30-37. doi: 10.11648/j.pamj.s.2014030602.16

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@article{10.11648/j.pamj.s.2014030602.16,
  author = {Francisco Bulnes and Ronin Goborov},
  title = {Integral Geometry and Complex Space-Time Cohomology in Field Theory},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {6-2},
  pages = {30-37},
  doi = {10.11648/j.pamj.s.2014030602.16},
  url = {https://doi.org/10.11648/j.pamj.s.2014030602.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030602.16},
  abstract = {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.},
 year = {2014}
}

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TY  - JOUR
T1  - Integral Geometry and Complex Space-Time Cohomology in Field Theory
AU  - Francisco Bulnes
AU  - Ronin Goborov
Y1  - 2014/12/27
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.s.2014030602.16
DO  - 10.11648/j.pamj.s.2014030602.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
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AB  - 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.
VL  - 3
IS  - 6-2
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Author Information

Francisco Bulnes

Head of Research Department in Mathematics and Engineering, TESCHA, Chalco, Mexico
Ronin Goborov

Department of Mathematics, Lomonosov University, Moscu, Russia

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APA Style

Francisco Bulnes, Ronin Goborov. (2014). Integral Geometry and Complex Space-Time Cohomology in Field Theory. Pure and Applied Mathematics Journal, 3(6-2), 30-37. https://doi.org/10.11648/j.pamj.s.2014030602.16

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ACS Style

Francisco Bulnes; Ronin Goborov. Integral Geometry and Complex Space-Time Cohomology in Field Theory. Pure Appl. Math. J. 2014, 3(6-2), 30-37. doi: 10.11648/j.pamj.s.2014030602.16

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AMA Style

Francisco Bulnes, Ronin Goborov. Integral Geometry and Complex Space-Time Cohomology in Field Theory. Pure Appl Math J. 2014;3(6-2):30-37. doi: 10.11648/j.pamj.s.2014030602.16

Copy | Download

@article{10.11648/j.pamj.s.2014030602.16,
  author = {Francisco Bulnes and Ronin Goborov},
  title = {Integral Geometry and Complex Space-Time Cohomology in Field Theory},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {6-2},
  pages = {30-37},
  doi = {10.11648/j.pamj.s.2014030602.16},
  url = {https://doi.org/10.11648/j.pamj.s.2014030602.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030602.16},
  abstract = {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.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Integral Geometry and Complex Space-Time Cohomology in Field Theory
AU  - Francisco Bulnes
AU  - Ronin Goborov
Y1  - 2014/12/27
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.s.2014030602.16
DO  - 10.11648/j.pamj.s.2014030602.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 30
EP  - 37
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.s.2014030602.16
AB  - 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.
VL  - 3
IS  - 6-2
ER  -

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