Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics

Francisco Bulnes

doi:doi:10.11648/j.ajea.20150306.12

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Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics

Francisco Bulnes

Published in American Journal of Electromagnetics and Applications (Volume 3, Issue 6)

Received: 24 September 2015 Accepted: 7 October 2015 Published: 19 October 2015

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Abstract

Through consider applications of the (, K)- modules as £- modules to the Lie groups SL(2, R), SU(2), SO(4), U(4, R), SU(2, 2), SO(4, R), SU(p, q), and Sp(n, K), the evaluating of integrals on equivariant and invariant holomorphic vector bundles under the action of these groups, are created and developed electromagnetic models of the space-time with their field observable obtained as images of integral transforms that are solutions of the field equations modulo electromagnetic fields. Finally is constructed through the equivalences obtained by these integral transforms the moduli space involving the non-commutative rings in electro-physics.

Published in	American Journal of Electromagnetics and Applications (Volume 3, Issue 6)
DOI	10.11648/j.ajea.20150306.12
Page(s)	43-52
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), 2015. Published by Science Publishing Group

Keywords

Electromagnetic Space-Time Models, Electromagnetic Intertwining Operators, Mathematical Electrodynamics, Maxwell Fields, Ultra-Hyperbolic Wave Equation

References

[1]	F. Bulnes, Integral Geometry Methods on Deformed Categories in Field Theory II, 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. 1-5. doi: 10.11648/j.pamj.s.2014030602.11
[2]	F. 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
[3]	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.
[4]	M. Ramírez, L. Ramírez, O. Ramírez and F. Bulnes, “Energy-Time: Topological Quantum Diffeomorphisms in Field Theory,” Journal on Photonics and Spintronics (accepted) June, 2014.
[5]	A-Wollmann Kleinert, F. Bulnes “Leptons, the subtly Fermions and their Lagrangians for Spinor Fields: Their Integration in the Electromagnetic Strengthening,” Journal on Photonics and Spintronics, Vol 2 (1), pp12-21.
[6]	F. Bulnes, Research on Curvature of Homogeneous Spaces, TESCHA, Mexico, 2010, pp. 44-66. http://www.magnamatematica.org
[7]	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
[8]	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.
[9]	Bulnes, F. Martínez, I, Mendoza, A. Landa, M., “Design and Development of an Electronic Sensor to Detect and Measure Curvature of Spaces Using Curvature Energy,” Journal of Sensor Technology, 2012, 2, pp116-126. http://dx.doi.org/10.4236/jst.2012.23017.
[10]	F. Bulnes, “Curvature Spectrum to 2-Dimensional Flat and Hyperbolic Spaces through Integral Transforms,” Journal of Mathematics, Vol 1 (1), pp17-24.
[11]	Eastwood, M. G.; Ginsberg, M. L. Duality in twistor theory. Duke Math. J. 48 (1981), no. 1, 177--196. doi: 10.1215/S0012-7094-81-04812-2.
[12]	M. Eastwood, Notes on conformal differential geometry, The Proceedings of the 15^th Winter School “Geometry and Physics” (Srni 1995). Rend. Circ Mat. Palermo (2) Suppl. 43 (1996), 57-76.
[13]	D. Meise, Relations between 2D and 4D Conformal Quantum Field Theory, PhD Thesis, Institute for Theoretical Physics Georg-August-Universität Göttingen, Germany, 2010.
[14]	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. http://dx.doi.org/10.4236/jamp.2014.25019.
[15]	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.
[16]	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
[17]	I. E. Segal, Mathematical cosmology and extragalactic astronomy. Bull. Amer. Math. Soc. 83 (1977), no. 4.
[18]	Baston R. J., Eastwood, M. G., The Penrose transform: its interaction with representation theory Oxford Mathematical Monographs, Clarendon Press, Oxford 1989.
[19]	F. Bulnes and A. Álvarez, "Homological Electromagnetism and Electromagnetic Demonstrations on the Existence of Superconducting Effects Necessaries to Magnetic Levitation/Suspension," Journal of Electromagnetic Analysis and Applications, Vol. 5 No. 6, 2013, pp. 255-263. doi: 10.4236/jemaa. 2013. 56041.

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Francisco Bulnes. (2015). Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics. American Journal of Electromagnetics and Applications, 3(6), 43-52. https://doi.org/10.11648/j.ajea.20150306.12

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ACS Style

Francisco Bulnes. Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics. Am. J. Electromagn. Appl. 2015, 3(6), 43-52. doi: 10.11648/j.ajea.20150306.12

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AMA Style

Francisco Bulnes. Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics. Am J Electromagn Appl. 2015;3(6):43-52. doi: 10.11648/j.ajea.20150306.12

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@article{10.11648/j.ajea.20150306.12,
  author = {Francisco Bulnes},
  title = {Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics},
  journal = {American Journal of Electromagnetics and Applications},
  volume = {3},
  number = {6},
  pages = {43-52},
  doi = {10.11648/j.ajea.20150306.12},
  url = {https://doi.org/10.11648/j.ajea.20150306.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajea.20150306.12},
  abstract = {Through consider applications of the (, K)- modules as £- modules to the Lie groups SL(2, R), SU(2), SO(4), U(4, R), SU(2, 2), SO(4, R), SU(p, q), and Sp(n, K), the evaluating of integrals on equivariant and invariant holomorphic vector bundles under the action of these groups, are created and developed electromagnetic models of the space-time with their field observable obtained as images of integral transforms that are solutions of the field equations modulo electromagnetic fields. Finally is constructed through the equivalences obtained by these integral transforms the moduli space involving the non-commutative rings in electro-physics.},
 year = {2015}
}

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TY  - JOUR
T1  - Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics
AU  - Francisco Bulnes
Y1  - 2015/10/19
PY  - 2015
N1  - https://doi.org/10.11648/j.ajea.20150306.12
DO  - 10.11648/j.ajea.20150306.12
T2  - American Journal of Electromagnetics and Applications
JF  - American Journal of Electromagnetics and Applications
JO  - American Journal of Electromagnetics and Applications
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PB  - Science Publishing Group
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AB  - Through consider applications of the (, K)- modules as £- modules to the Lie groups SL(2, R), SU(2), SO(4), U(4, R), SU(2, 2), SO(4, R), SU(p, q), and Sp(n, K), the evaluating of integrals on equivariant and invariant holomorphic vector bundles under the action of these groups, are created and developed electromagnetic models of the space-time with their field observable obtained as images of integral transforms that are solutions of the field equations modulo electromagnetic fields. Finally is constructed through the equivalences obtained by these integral transforms the moduli space involving the non-commutative rings in electro-physics.
VL  - 3
IS  - 6
ER  -

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Author Information

Francisco Bulnes

Research Department in Mathematics and Engineering, TESCHA, Chalco, Mexico

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APA Style

Francisco Bulnes. (2015). Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics. American Journal of Electromagnetics and Applications, 3(6), 43-52. https://doi.org/10.11648/j.ajea.20150306.12

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ACS Style

Francisco Bulnes. Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics. Am. J. Electromagn. Appl. 2015, 3(6), 43-52. doi: 10.11648/j.ajea.20150306.12

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AMA Style

Francisco Bulnes. Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics. Am J Electromagn Appl. 2015;3(6):43-52. doi: 10.11648/j.ajea.20150306.12

Copy | Download

@article{10.11648/j.ajea.20150306.12,
  author = {Francisco Bulnes},
  title = {Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics},
  journal = {American Journal of Electromagnetics and Applications},
  volume = {3},
  number = {6},
  pages = {43-52},
  doi = {10.11648/j.ajea.20150306.12},
  url = {https://doi.org/10.11648/j.ajea.20150306.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajea.20150306.12},
  abstract = {Through consider applications of the (, K)- modules as £- modules to the Lie groups SL(2, R), SU(2), SO(4), U(4, R), SU(2, 2), SO(4, R), SU(p, q), and Sp(n, K), the evaluating of integrals on equivariant and invariant holomorphic vector bundles under the action of these groups, are created and developed electromagnetic models of the space-time with their field observable obtained as images of integral transforms that are solutions of the field equations modulo electromagnetic fields. Finally is constructed through the equivalences obtained by these integral transforms the moduli space involving the non-commutative rings in electro-physics.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Electrodynamics: Groups, Cohomology Classes, Unitary Representations, Orbits and Integral Transforms in Electro-Physics
AU  - Francisco Bulnes
Y1  - 2015/10/19
PY  - 2015
N1  - https://doi.org/10.11648/j.ajea.20150306.12
DO  - 10.11648/j.ajea.20150306.12
T2  - American Journal of Electromagnetics and Applications
JF  - American Journal of Electromagnetics and Applications
JO  - American Journal of Electromagnetics and Applications
SP  - 43
EP  - 52
PB  - Science Publishing Group
SN  - 2376-5984
UR  - https://doi.org/10.11648/j.ajea.20150306.12
AB  - Through consider applications of the (, K)- modules as £- modules to the Lie groups SL(2, R), SU(2), SO(4), U(4, R), SU(2, 2), SO(4, R), SU(p, q), and Sp(n, K), the evaluating of integrals on equivariant and invariant holomorphic vector bundles under the action of these groups, are created and developed electromagnetic models of the space-time with their field observable obtained as images of integral transforms that are solutions of the field equations modulo electromagnetic fields. Finally is constructed through the equivalences obtained by these integral transforms the moduli space involving the non-commutative rings in electro-physics.
VL  - 3
IS  - 6
ER  -

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