Electromagnetic Gauges and Maxwell Lagrangians Applied to the Determination of Curvature in the Space-Time and their Applications

Affiliation(s)

Department of Research in Mathematics and Engineering, Technological Institute of High Studies of Chalco, Chalco, Mexico..

Department of Research in Mathematics and Engineering, Technological Institute of High Studies of Chalco, Chalco, Mexico..

ABSTRACT

If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geometrical space on these geodesic (using the light caused from these points (charges) acting with the infinite null of gravitational field (background)) we can establish a model of the curvature through gauges inside the electromagnetic context. In partular this point of view is useful when it is about to go on in a quantized version from the curvature where the space is distorted by the interactions between particles. This demonstrates that curvature and torsion effect in the space-time are caused in the quantum dimension as back-reaction effects in photon propagation. Also this permits the observational verification and encodes of the gravity through of light fields deformations. The much theoretical information obtained using the observable effects like distortions is used to establish inside this Lagrangian context a classification of useful spaces of electro-dynamic configuration for the description of different interactions of field in the Universe related with gravity. We propose and design one detector of curvature using a cosmic censor of the space-time developed through distortional 3-dimensional sphere. Some technological applications of the used methods are exhibited.

If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geometrical space on these geodesic (using the light caused from these points (charges) acting with the infinite null of gravitational field (background)) we can establish a model of the curvature through gauges inside the electromagnetic context. In partular this point of view is useful when it is about to go on in a quantized version from the curvature where the space is distorted by the interactions between particles. This demonstrates that curvature and torsion effect in the space-time are caused in the quantum dimension as back-reaction effects in photon propagation. Also this permits the observational verification and encodes of the gravity through of light fields deformations. The much theoretical information obtained using the observable effects like distortions is used to establish inside this Lagrangian context a classification of useful spaces of electro-dynamic configuration for the description of different interactions of field in the Universe related with gravity. We propose and design one detector of curvature using a cosmic censor of the space-time developed through distortional 3-dimensional sphere. Some technological applications of the used methods are exhibited.

KEYWORDS

Back-reaction Effects, Electromagnetic Bundles, Form Operator, Electro-Gravitational Detectors, Maxwell’s Lagrangian, Quantum Curvature

Back-reaction Effects, Electromagnetic Bundles, Form Operator, Electro-Gravitational Detectors, Maxwell’s Lagrangian, Quantum Curvature

Cite this paper

F. Bulnes, "Electromagnetic Gauges and Maxwell Lagrangians Applied to the Determination of Curvature in the Space-Time and their Applications,"*Journal of Electromagnetic Analysis and Applications*, Vol. 4 No. 6, 2012, pp. 252-266. doi: 10.4236/jemaa.2012.46035.

F. Bulnes, "Electromagnetic Gauges and Maxwell Lagrangians Applied to the Determination of Curvature in the Space-Time and their Applications,"

References

[1] F. Bulnes, “Design of Measurement and Detection Devices of Curvature through of the Synergic Integral Operators of the Mechanics on Light Waves,” International Mechanical Engineering Congress and Exposition, Lake Buena Vista, 13-19 November 2009, pp. 91-102. doi:10.1115/IMECE2009-10038

[2] F. Bulnes, “Analytic Dissertations of the Sidereal Hyperspace,” Masterful Conference in UTM, Insurgents University, Mexico City, 1996, pp. 23-98.

[3] F. Bulnes, “Radon Transform and the Curvature of One Universe,” Master’s Thesis, National Autonomous University of Mexico, Mexico City, 2001.

[4] F. Bulnes, “Cohomology of Moduli Spaces in Differential Operators Classification to the Field Theory,” Proceedings of the 8th International Conference on Function Spaces, Differential Operators and Nonlinear Analysis, Tabarz, Thür, 18-24 September 2011, pp. 81101-81119.

[5] F. Bulnes, “Doctoral Course of Mathematical Electrodynamics,” Internal. Proc. Appliedmath, Vol. 2, 2006, pp. 398-447.

[6] S. Kobayashi and K. Nomizu, “Foundations of Differential Geometry, Vol. 1,” John Wiley and Sons, New York, 1963.

[7] S. Kobayashi, K. Nomizu, “Foundations of Differential Geometry, Vol. 2,” Wiley and Sons, New York, 1969.

[8] L. K. Landau, E. Lifschitz, “The Classical Theory of Fields,” Addison-Wesley, Cambridge, 1951

[9] L. J. Mason, “A Hamiltonian Interpretation of Penrose’s Quasi-Local Mass,” Classical and Quantum Gravity, Vol. 6, No. 2, L-7-L13, 1989. doi:10.1088/0264-9381/6/2/001

[10] L. J. Mason and J. Frauendiener, “Sparling 3-Form, Ashtekar Variables and Quasi-Local Mass,” Twistor, Twistor in Mathematics and Physics, Cambrindge, 1990.

[11] R. Penrose, “Quasilocal Mass and Angular Momentum in General Relativity,” Proceedings of the Royal Society A, Vol. 381, No. 1780, 1982, pp. 53-63. doi:10.1098/rspa.1982.0058

[12] G. Giachetta and G. Sardanashvily, “Stress-Energy-Momentum Tensors in Lagrangian Field Theory. Part 2. Gravitational Superpotential,” 1995. http://arxiv.org/abs/gr-qc/9511040v1

[13] H. Friedrich, “Gravitational Fields Near Space-Like and Null Infinity”, Journal of Geometry and Physics, Vol. 24, No. 2, 1998, pp. 83-163. doi:10.1016/S0393-0440(97)82168-7

[14] J. D. E. Creighton and R. Mann, “Quasilocal Thermodynamics of Dilaton Gravity Coupled to Gauge Fields,” Physical Review D, Vol. 52, No. 8, 1995, pp. 4569-4587. doi:10.1103/PhysRevD.52.4569

[15] J. Król, “Quantum Gravity Insights from Smooth 4-Geometries on Trivial R4,” Quantum Gravity, 2012. pp. 5378.

[16] J. Krol, “(Quantum) Gravity Effects via Exotic R4,” Annalen der Physik, Vol. 19, No. 3-5, 2010, pp. 355-358. doi:10.1002/andp.201010446

[17] N. Prezas and K. Sfetsos, “Supersymmetric Moduli of the SU(2) × Rφ Linear Dilaton Background and NS5-Branes,” 2008. http://iopscience.iop.org/1126-6708/2008/06/080/pdf/1126-6708_2008_06_080.pdf

[18] E. Kiritsis and C. Kounnas, “Infrared Behavior of Closed Superstrings in Strong Magnetic and Gravitational Fields,” Nuclear Physics B, Vol. 456, No. 3, 1995, pp. 699-731. doi:10.1016/0550-3213(95)00540-2

[19] S. Hassan and A. Sen, “Marginal Deformations of WZNW and Coset Models from O(d, d) Transformation,” Nuclear Physics B, Vol. 405, No. 1, 1993, pp. 143-165. doi:10.1016/0550-3213(93)90429-S

[20] J. Frauendiener, “On the Penrose Inequality,” Physical Review Letters, Vol. 87, No. 100, 2001. doi:10.1103/PhysRevLett.87.101101

[21] M. F. Parisi, “Propagation of Photons in Quantum Gravity,” Ph.D. Thesis, National Córdoba University, Córdoba, 2007.

[22] G. W. Gibbons, “The Isoperimetric and Bogomolny Inequalities for Black Holes,” In: T. J. Willmore and N. J. Hitchin, Eds., Global Riemannian Geometry, Ellis Horwood Halsted Press, Chichester, 1984, pp. 194-202.

[23] R. Geroch, “Asymptotic Structure of Space-Time,” Proceedings of a Symposium on Asymptotic Structure of Space-Time, Cincinnati, 14-18 June 1976, pp. 1-105.

[24] R. M. Kelly, “Asymptotically Anti-De Sitter Space-Time,” Twistor Newsletter, Vol. 20, 1985, pp. 11-23.

[25] K. P. Tod, “Penrose’s Quasilocal Mass and Isoperimetric Inequality for Static Black Holes Class,” Classical and Quantum Gravity, Vol. 2, No. 4, 1985, pp. L65-L68. doi:10.1088/0264-9381/2/4/001

[26] J. Frauendiener and L. B. Szabados, “The Kernel of the Edth Operators on Higher-Genus Spacelike 2-Surfaces,” Classical and Quantum Gravity, Vol. 18, No. 6, 2001, pp. 1003-1014. doi:10.1088/0264-9381/18/6/303

[27] V. Schomerus, “Lectures on Branes in Curved Backgrounds,” Classical and Quantum Gravity, Vol. 19, No. 22, 2002, p. 5781. doi:10.1088/0264-9381/19/22/305

[28] A. J. Dougan, “Quasi-Local Mass for Spheres,” Classical and Quantum Gravity, Vol. 9, No. 11, 1992, pp. 24612475. doi:10.1088/0264-9381/9/11/012

[29] N. M. J. Woudhouse, “Cylindrical Gravitational Waves Class,” Classical and Quantum Gravity, Vol. 6, No. 6, 1989, pp. 933-943. doi:10.1088/0264-9381/6/6/017

[30] Y. Aharonov and D. Bohm, “Significance of Electromagnetic Potentials in Quantum Theory,” Physical Review, Vol. 115, No. 3, 1959, pp. 485-491. doi:10.1103/PhysRev.115.485

[31] F. Bulnes, “Lagrangian Dynamics and Electromagnetic Gauges Applied to the Determination of Curvature of One Universe,” Proceedings of Internal 6th Canadian Centre for Isotopic Microanalysis, Habana, 2010, pp. 242-248.

[32] C. Ortix, S. O. G. Kiravittaya, O. G. Schmidt and J. Van den Brink, “Curvature-Induced Geometric Potential in Strain-Driven Nanostructures,” Physical Review B, Vol. 84, No. 4, 2011, Article ID: 045438. doi:10.1103/PhysRevB.84.045438

[33] G. F. Smoot, “Cosmic Microwave Background Radiation Anisotropies: Their Discovery and Utilization,” Nobel Lecture, Nobel Foundation, 2006. http://nobelprize.org/nobel_prizes/physics/laureates/2006/smoot-lecture.html

[34] E. Kiritsis and C. Kounnasa, “Curved Four-Dimensional Space-Time as Infrared Regulator in Superstring Theories,” Nuclear Physics B—Proceedings Supplements, Vol. 41, No. 1-3, 1995, pp. 331-340. doi:10.1016/0920-5632(95)00441-B

[35] Smoot Group, “The Cosmic Microwave Background Radiation,” Lawrence Berkeley National Laboratory, Berkeley ,2008.

[1] F. Bulnes, “Design of Measurement and Detection Devices of Curvature through of the Synergic Integral Operators of the Mechanics on Light Waves,” International Mechanical Engineering Congress and Exposition, Lake Buena Vista, 13-19 November 2009, pp. 91-102. doi:10.1115/IMECE2009-10038

[2] F. Bulnes, “Analytic Dissertations of the Sidereal Hyperspace,” Masterful Conference in UTM, Insurgents University, Mexico City, 1996, pp. 23-98.

[3] F. Bulnes, “Radon Transform and the Curvature of One Universe,” Master’s Thesis, National Autonomous University of Mexico, Mexico City, 2001.

[4] F. Bulnes, “Cohomology of Moduli Spaces in Differential Operators Classification to the Field Theory,” Proceedings of the 8th International Conference on Function Spaces, Differential Operators and Nonlinear Analysis, Tabarz, Thür, 18-24 September 2011, pp. 81101-81119.

[5] F. Bulnes, “Doctoral Course of Mathematical Electrodynamics,” Internal. Proc. Appliedmath, Vol. 2, 2006, pp. 398-447.

[6] S. Kobayashi and K. Nomizu, “Foundations of Differential Geometry, Vol. 1,” John Wiley and Sons, New York, 1963.

[7] S. Kobayashi, K. Nomizu, “Foundations of Differential Geometry, Vol. 2,” Wiley and Sons, New York, 1969.

[8] L. K. Landau, E. Lifschitz, “The Classical Theory of Fields,” Addison-Wesley, Cambridge, 1951

[9] L. J. Mason, “A Hamiltonian Interpretation of Penrose’s Quasi-Local Mass,” Classical and Quantum Gravity, Vol. 6, No. 2, L-7-L13, 1989. doi:10.1088/0264-9381/6/2/001

[10] L. J. Mason and J. Frauendiener, “Sparling 3-Form, Ashtekar Variables and Quasi-Local Mass,” Twistor, Twistor in Mathematics and Physics, Cambrindge, 1990.

[11] R. Penrose, “Quasilocal Mass and Angular Momentum in General Relativity,” Proceedings of the Royal Society A, Vol. 381, No. 1780, 1982, pp. 53-63. doi:10.1098/rspa.1982.0058

[12] G. Giachetta and G. Sardanashvily, “Stress-Energy-Momentum Tensors in Lagrangian Field Theory. Part 2. Gravitational Superpotential,” 1995. http://arxiv.org/abs/gr-qc/9511040v1

[13] H. Friedrich, “Gravitational Fields Near Space-Like and Null Infinity”, Journal of Geometry and Physics, Vol. 24, No. 2, 1998, pp. 83-163. doi:10.1016/S0393-0440(97)82168-7

[14] J. D. E. Creighton and R. Mann, “Quasilocal Thermodynamics of Dilaton Gravity Coupled to Gauge Fields,” Physical Review D, Vol. 52, No. 8, 1995, pp. 4569-4587. doi:10.1103/PhysRevD.52.4569

[15] J. Król, “Quantum Gravity Insights from Smooth 4-Geometries on Trivial R4,” Quantum Gravity, 2012. pp. 5378.

[16] J. Krol, “(Quantum) Gravity Effects via Exotic R4,” Annalen der Physik, Vol. 19, No. 3-5, 2010, pp. 355-358. doi:10.1002/andp.201010446

[17] N. Prezas and K. Sfetsos, “Supersymmetric Moduli of the SU(2) × Rφ Linear Dilaton Background and NS5-Branes,” 2008. http://iopscience.iop.org/1126-6708/2008/06/080/pdf/1126-6708_2008_06_080.pdf

[18] E. Kiritsis and C. Kounnas, “Infrared Behavior of Closed Superstrings in Strong Magnetic and Gravitational Fields,” Nuclear Physics B, Vol. 456, No. 3, 1995, pp. 699-731. doi:10.1016/0550-3213(95)00540-2

[19] S. Hassan and A. Sen, “Marginal Deformations of WZNW and Coset Models from O(d, d) Transformation,” Nuclear Physics B, Vol. 405, No. 1, 1993, pp. 143-165. doi:10.1016/0550-3213(93)90429-S

[20] J. Frauendiener, “On the Penrose Inequality,” Physical Review Letters, Vol. 87, No. 100, 2001. doi:10.1103/PhysRevLett.87.101101

[21] M. F. Parisi, “Propagation of Photons in Quantum Gravity,” Ph.D. Thesis, National Córdoba University, Córdoba, 2007.

[22] G. W. Gibbons, “The Isoperimetric and Bogomolny Inequalities for Black Holes,” In: T. J. Willmore and N. J. Hitchin, Eds., Global Riemannian Geometry, Ellis Horwood Halsted Press, Chichester, 1984, pp. 194-202.

[23] R. Geroch, “Asymptotic Structure of Space-Time,” Proceedings of a Symposium on Asymptotic Structure of Space-Time, Cincinnati, 14-18 June 1976, pp. 1-105.

[24] R. M. Kelly, “Asymptotically Anti-De Sitter Space-Time,” Twistor Newsletter, Vol. 20, 1985, pp. 11-23.

[25] K. P. Tod, “Penrose’s Quasilocal Mass and Isoperimetric Inequality for Static Black Holes Class,” Classical and Quantum Gravity, Vol. 2, No. 4, 1985, pp. L65-L68. doi:10.1088/0264-9381/2/4/001

[26] J. Frauendiener and L. B. Szabados, “The Kernel of the Edth Operators on Higher-Genus Spacelike 2-Surfaces,” Classical and Quantum Gravity, Vol. 18, No. 6, 2001, pp. 1003-1014. doi:10.1088/0264-9381/18/6/303

[27] V. Schomerus, “Lectures on Branes in Curved Backgrounds,” Classical and Quantum Gravity, Vol. 19, No. 22, 2002, p. 5781. doi:10.1088/0264-9381/19/22/305

[28] A. J. Dougan, “Quasi-Local Mass for Spheres,” Classical and Quantum Gravity, Vol. 9, No. 11, 1992, pp. 24612475. doi:10.1088/0264-9381/9/11/012

[29] N. M. J. Woudhouse, “Cylindrical Gravitational Waves Class,” Classical and Quantum Gravity, Vol. 6, No. 6, 1989, pp. 933-943. doi:10.1088/0264-9381/6/6/017

[30] Y. Aharonov and D. Bohm, “Significance of Electromagnetic Potentials in Quantum Theory,” Physical Review, Vol. 115, No. 3, 1959, pp. 485-491. doi:10.1103/PhysRev.115.485

[31] F. Bulnes, “Lagrangian Dynamics and Electromagnetic Gauges Applied to the Determination of Curvature of One Universe,” Proceedings of Internal 6th Canadian Centre for Isotopic Microanalysis, Habana, 2010, pp. 242-248.

[32] C. Ortix, S. O. G. Kiravittaya, O. G. Schmidt and J. Van den Brink, “Curvature-Induced Geometric Potential in Strain-Driven Nanostructures,” Physical Review B, Vol. 84, No. 4, 2011, Article ID: 045438. doi:10.1103/PhysRevB.84.045438

[33] G. F. Smoot, “Cosmic Microwave Background Radiation Anisotropies: Their Discovery and Utilization,” Nobel Lecture, Nobel Foundation, 2006. http://nobelprize.org/nobel_prizes/physics/laureates/2006/smoot-lecture.html

[34] E. Kiritsis and C. Kounnasa, “Curved Four-Dimensional Space-Time as Infrared Regulator in Superstring Theories,” Nuclear Physics B—Proceedings Supplements, Vol. 41, No. 1-3, 1995, pp. 331-340. doi:10.1016/0920-5632(95)00441-B

[35] Smoot Group, “The Cosmic Microwave Background Radiation,” Lawrence Berkeley National Laboratory, Berkeley ,2008.