ON QUANTUM BLACK HOLE SOLUTIONS OF QUANTUM SUPER YANG-MILLS EQUATIONS

Agostino Prástaro

ABSTRACT. The category of quantum super manifolds, introduced by A.Prástaro, gives us a natural framework where implement a geometric theory of quantum super partial differential equations (PDE's). (See refs.[1-15].) The interest for quantum supermanifolds is motivated by the fact that these structures allow us to describe the unification of all the four fundamental forces (gravity, electromagnetic, weak nuclear, strong nuclear), at the quantum level. In fact, by means of quantum supermanifolds we can unify in an unique noncommutative manifold, the apparent different concepts of electro-weak force and strong-quantum-gravity force. Quantum supermanifolds play in the mathematical description of microscopic worlds a role similar to one played by Riemannian manifolds in General Relativity.

Therefore, the geometric theory of quantum super PDE's developed by A.Prástaro in refs.[1-15], gives us a mathematical tool with which formulate the quantum field theory and identify very sophisticated solutions, able to interpretate very complex phenomena. Furthermore, string-like objects (extendons) can be well described in such a mathematical formulation, like p-chain solutions of quantum super PDE's.

In this talk we aim present some recent developments in this direction. In particular we will consider quantum black holes as solutions of quantum super Yang-Mills equations. These interpret very high energy level production of particles, where the effects of strong-quantum-gravity become dominant. In such a way the strong nuclear force is identified with quantum-(super)gravity, and quantum black hole solutions, are just quantum-(super)gravity in action.

References

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A. Prástaro, Geometry of PDEs and Mechanics, World Scientific Publishing Co., Singapore, 1996, 760 pp.

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A. Prástaro, (Co)bordisms in PDE's and quantum PDE's, Rep. Math. Phys., 38(3):443-455, 1996.

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A. Prástaro, Quantum and integral (co)bordism groups in partial differential equations, Acta Appl. Math., 51(3):243-302, 1998.

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A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math., 59(2):111-202, 1999.

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A. Prástaro, (Co)bordism groups in quantum PDE's, Acta Appl. Math., 64(2/3):111-217, 2000.

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A. Prástaro, Quantum manifolds and integral (co)bordism groups in quantum partial differential equations, Nonlinear Analysis, 47/4:2609-2620, 2001.

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A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co., 2004, 500 pp.

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A. Prástaro, Quantum super Yang-Mills equations: Global existence and mass-gap, Dynamic Systems & Applications, 4:227-234, 2004.

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A. Prástaro, Conservation laws in quantum super PDE's, Proceedings of the Conference on Differential & Difference Equations and Applications, Hindawi Publishing Corporation, New York (2006), 1-10.

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A. Prástaro, (Co)bordism groups in quantum super PDE's. I: Quantum supermanifolds, Nonlinear Analysis: Real World Appls. DOI: 101016/j.nonrwa.2005.12.008 (in press).

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A. Prástaro, (Co)bordism groups in quantum super PDE's. II: Quantum super PDE's, Nonlinear Analysis: Real World Appls. DOI: 101016/j.nonrwa.2005.12.007 (in press).

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A. Prástaro, (Co)bordism groups in quantum super PDE's. III: Quantum super Yang-Mills equations, Nonlinear Analysis: Real World Appls. DOI: 101016/j.nonrwa.2005.12.005 (in press).

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A. Prástaro, Algebraic topology in constraint variational equations, Short communication in Topology, ICM 2006, Madrid, Spain, August 30, 2006, (preprint).

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A. Prástaro, On the algebraic topology of PDE's, ICM 2006 Satellite Conference Advances in PDE's Geometry, Madrid, Spain, August 31 - September 2, 2006, (preprint).

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A. Prástaro and Th. M. Rassias, A geometric approach to a noncommutative generalized d'Alembert equation, C. R. Acad. Sci. Paris, 330(I-7):545-550, 2000; Results on the J.D'Alembert equation, Ann Acad. Paed. Crac. Stud. Math., 1:117-128, 2001.