Mathematical Nanotechnology: Quantum Field Intentionality


Considering the finite actions of a field on the matter and the space which used to infiltrate their quantum reality at level particle, methods are developed to serve to base the concept of intentional action of a field and their ordered and supported effects (synergy) that must be realized for the organized transformation of the space and matter. Using path integrals, these transformations are decoded and their quantum principles are shown.

Share and Cite:

Bulnes, F. (2013) Mathematical Nanotechnology: Quantum Field Intentionality. Journal of Applied Mathematics and Physics, 1, 25-44. doi: 10.4236/jamp.2013.15005.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. E. Marsden and R. Abraham, “Manifolds, Tensor Analysis and Applications,” Addison-Wesley, Massachusetts, 1993.
[2] C. Chevalley, “Theory of Lie Groups,” Princeton University Press, Princeton, 1946.
[3] F. E. Burstall and J. H. Rawnsley, “Twistor Theory for Riemannian Symmetric Spaces,” Springer Verlag, New York, 1990.
[4] F. Bulnes, “Analysis of Prospective and Development of Effective Technologies through Integral Synergic Operators of the Mechanics,” The 14th Scientific Convention of Engineering and Arquitecture: Proceedings of the 5th Cuban Congress of Mechanical Engineering, 2-5 December 2008, Havana.
[5] W. Rudin, “Functional Analysis,” McGraw Hill Education, New York, 1973.
[6] F. Bulnes, H. F. Bulnes, E. Hernandez and J. Maya, “Diagnosis and Spectral Encoding in Integral Medicine through Electronic Devices Designed and Developed by Path Integrals,” Journal of Nanotechnology in Engineering and Medicine, Vol. 2, No. 2, 2011, Article ID: 021009.
[7] F. Bulnes, “Theoretical Concepts of Quantum Mechanics,” In: M. R. Pahlavani, Ed., Correction, Alignment, Restoration and Re-Composition of Quantum Mechanical Fields of Particles by Path Integrals and Their Applications, InTech, Rijeka, 2012.
[8] M. Alonso and E. Finn, “Fundamental University Physics, Volume III: Quantum Statistical Physics,” Addison-Wesley Publishing Co., Massachusetts, 1968.
[9] R. P. Feynman, “Space-Time Approach to Non-Relativistic Quantum Mechanics,” Reviews of Modern Physics, Vol. 20, No. 2, 1948, pp. 367-387.
[10] F. Bulnes, “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, 2011), Vol. 1, No. 12, 2011, pp. 1-22.
[11] F. Bulnes, H. F. Bulnes and D. Cote, “Symptom Quantum Theory: Loops and Nodes in Psychology and Nanometric Actions by Quantum Medicine on the Mind Mechanisms Programming Path Integrals,” Journal of Smart Nanosystems in Engineering and Medicine, Vol. 1, No. 1, 2012, pp. 97-121.
[12] F. Bulnes, “Quantum Intentionality and Determination of Realities in the Space-Time through Path Integrals and Their Integral Transforms,” In: P. Bracken, Ed., Advances in Quantum Mechanics, InTech, Rijeka, 2013.
[13] H. B. Lawson and M. L. Michelsohn, “Spin Geometry,” Princeton University Press, Princeton, 1989.
[14] J. Schwinger, “Particles, Sources, and Fields,” Vol. 1, 3rd Edition, Advanced Book Program, Perseus Books, Massachusetts, 1998.
[15] R. P. Feynman, R. B. Leighton and M. Sands, “Electromagnetism and matter,” Vol. II, Addison-Wesley, Massachusetts, 1964.
[16] F. Bulnes and M. Shapiro, “On General Theory of Integral Operators to Analysis and Geometry (Monograph in Mathematics),” 2007.
[17] F. Bulnes, H. F. Bulnes, E. Hernandez and J. Maya, “Integral Medicine: New Methods of Organ-Regeneration by Cellular Encoding through Path Integrals applied to the Quantum Medicine,” Journal of Nanotechnology in Engineering and Medicine, Vol. 1, No. 7, 2010, Article ID: 030019.
[18] D. McDuff and D. Salamon, “Introduction to Symplectic Topology,” Oxford University Press, Oxford, 1998.
[19] I. S. Sokolnikoff, “Tensor Analysis: Theory and Applications,” Wiley and Sons, New York, 1951.
[20] B. R. Holstein, “Topics in Advanced Quantum Mechanics,” Addison-Wesley Publishing Company, Cambridge 1992.
[21] A. Kapustin, M. Kreuser and K. G. Schlesinger, “Homological Mirror Symmetry: New Developments and Perspectives,” Springer, Berlin, 2009.
[22] Y. Aharonov and D. Bohm, “Significance of Electromagnetic Potentials in Quantum Theory,” Physical Review, Vol. 115, No. 3, 1959, pp. 485-491.
[23] F. Bulnes, “Doctoral Course of Mathematical Electrodynamics,” In: National Polytechnique Institute, Ed., Appliedmath 3: Advanced Courses, Proceedings of the Applied Mathematics International Congress, 25-29 October 2006, México.
[24] E. R. LeBrun, “Twistors, Ambitwistors and Conformal Gravity,” In: T. N. Bailey and R. J. Baston, Eds., Twistors in Mathematics and Physics, Cambridge University, Cambridge, 1990, pp. 71-86.
[25] L. P. Hughston and W. T. Shaw, “Classical Strings in Ten Dimensions,” Proceedings of the Royal Society of London Series A: Mathematical and Physical Sciences, Vol. 414. No. 1847, 1987, pp. 423-431.
[26] F. Bulnes, “Penrose Transform on D-Modules, Moduli Spaces and Field Theory,” Advances in Pure Mathematics, Vol. 2, No. 6, 2012, pp. 379-390.
[27] R. Sobreiro, “Quantum Gravity,” InTech, Rijeka, 2012.
[28] P. Griffiths and J. Harris, “Principles of Algebraic Geometry,” Wiley-Interscience, New York, 1994.
[29] M. Gross, D. Huybrechts and D. Joyce, “Calabi-Yau Manifolds and Related Geometries,” Springer, Norway, 2001.
[30] J. Hoogeveen and K. Skenderis, “Decoupling of Unphysical States in the Minimal Pure Spinor Formalism I,” 2010.
[31] N. Berkovits, J. Hoogeveen and K. Skenderis, “Decoupling of Unphysical States in the Minimal Pure Spinor Formalism II,” 2009.
[32] T. W. B. Kibbe, “Geometrization of Quantum Mechanics,” Springer Online Journal Archives, Vol. 65, No. 2, 1979, pp. 189-201.
[33] J. Jost, “Riemannian Geometry and Geometric Analysis,” 4th Edition, Springer-Verlag, Berlin, 2005.
[34] Y. Makeenko, “Methods of Contemporary Gauge Theory,” Cambridge University Press, Cambridge, 2002.
[35] F. Bulnes, “Treatise of Advanced Mathematics: System and Signals Analysis,” 1998.
[36] F. Bulnes and H. F. Bulnes, “Quantum Medicine Actions: Programming Path Integrals on Integral Mono-Pharmacists for Strengthening and Arranging of the Mind on Body,” Journal of Frontiers of Public Health, Vol. 1, No. 3, 2012, pp. 57-65.
[37] F. Bulnes, “Analysis and Design of Algorithms to the Master in Applied Informatics,” Research Course, University of Informatics Sciences (UCI), Habana, 2007.
[38] F. Bulnes, “Cohomology of Cycles and Integral Topology,” 2008.
[39] B. Simon and M. Reed, “Mathematical Methods for Physics,” Vol. 1, Academic Press, New York, 1972.
[40] F. Bulnes, “Conferences of Mathematics: Seminar of Representation Theory of Reductive Lie Groups,” Compilation of Institute of Mathematics, UNAM Publications, Mexico, 2000.
[41] F. Bulnes, “Handle of Scientific and Philosophical Methods of the Research: Guide of Prospective and Quality of the International Scientific and Technological Research,” 2011.
[42] J. Dieudonne, “Treatise on Analysis,” Vol. 6, Academic Press, New York, 1976.
[43] C. Truesdell and R. A. Topin, “The Classical Field Theories (in Encyclopaedia of Physics, Vol. III/1),” SpringerVerlag, Berlin, 1960.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.