Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

HEISENBERG GROUPS - A UNIFYING STRUCTURE OF SIGNAL THEORY, HOLOGRAPHY AND QUANTUM INFORMATION THEORY

  • Binz, Ernst (Lehrstuhl fur Mathematik I, Universitat Mannheim) ;
  • Pods, Sonja (Lehrstuhl fur Mathematik I, Universitat Mannheim) ;
  • Schempp, Walter (Lehrstuhl fur Mathematik I, Universitat Siegen)
  • 발행 : 2003.01.01

⟨ 이전 논문 다음 논문 ⟩

초록

Vector fields in three-space admit bundles of internal variables such as a Heisenberg algebra bundle. Information transmission along field lines of vector fields is described by a wave linked to the Schrodinger representation in the realm of time-frequency analysis. The preservation of local information causes geometric optics and a quantization scheme. A natural circle bundle models quantum information visualized by holographic methods. Features of this setting are applied to magnetic resonance imaging.

키워드

참고문헌

  1. Coherent States, Wavelets and Their Gneralications S. T. Ali;J. P. Antoine;J. -P. Gazeau
  2. An Introduction to Spinors and Geometry with Applications in Physics I. M. Benn;R. W. Tucker
  3. Differntial Geometry: Manifolds, Curves, and Surgaces v.GTM115 M. Berger;B. Gostiaux
  4. The geometry of Classical Fields, Mathematical Studies/ Notas de Matematica v.154 E. Binz;J. Sniatycki;H. Fischer
  5. Spinor Geometry and Signal Transmission, in preparation E, Binz;S. Pods;W, Schempp
  6. Computing Anticipatory Systems,CASYS 2001, (5th) International Conference, AIP Conference Proceddidngs v.327 Spinor Geometry and Signal Transmission in Three Space E. Binz;S. Pods;W. Schempp;D. Dubois(Ed.)
  7. Proc. (Fourth) International Workshop on Complex Structures and Vector fields: Aspects of Complex Analysis, Differntial Geometry, Mathematical Physical Physis, and Applicationsa Quantum Teleportation and Spin Echo: A Unitary Symplectic Spinor Approach E. Binz;W. Schempp
  8. Proc. of the Intern. Conference on Quantum Theory and Symmetries Ptojective Geometry and Keppler's Libration Theory E, Binz;W. Schempp
  9. Result. Math. v.37 Vector Fields in Three-Space, Natural Internal Degrees of Freedom, Signal Transmission and Quantization E. Binz;W. Schempp
  10. Proc. Leray Conference Entanglement Parataxy and Cosmology E. Binz;W. Schempp
  11. International Journal of Cimputing anticipatory Systmes v.7 Creating Magnetic Resonance Images E. Binz;W. Schempp;D. Dubois(Ed.)
  12. Cybernetic ans systems 2000 v.1 Qyantum Systems: Form Macro Systems to Micro Systems - the Holographic Technique E. Binz;W. Schempp;R. Trappl(Ed.)
  13. International Journal of Computing Anticipatory Systems v.10 Signal transmission Along Singularity Free Gradient Fields and Quantization Caused by Internal Degrees of Freedom E, Binz;W. Schempp;D. Dubois(Ed.)
  14. Informatica v.25 Information Technology: the Lie group defining the filter Banks of the Compact Disc E. Binz;W. Schempp
  15. Optik M. Born
  16. Principles of Optics, (7th ed.) M. Born;E. Wolf
  17. Elements of Information Theory T. M. Cover;J. A. Thomas
  18. Harmonic Analysis in Phase Space G. B. Folland
  19. Introduction to Matrix Methods in Optics A. Gerrard;J. M. Burch
  20. Lectures in Algebraic Topology A. Greenberg
  21. Pure and Applied Mathematics v.47 no.2 Connections, Curvature, and Co0homology W. Greub;S. Halperin;R. Vanstoce
  22. J. of Math. Phys v.16 no.6 Minimal Coupling and Complex Line Bundles W. Greub;H. Petry
  23. Foundations of Time-Frequency Analysis K. Grochenig
  24. Symplectic Techniques in Physics V. Guilemin;S. Sternberg
  25. Munich, (2nd ed.) E. Hexht;Optik, R. Oldenbourg
  26. Quantenmechanik v.Ⅲ Lehrbuch der Theoretischen Physik L. D. Landau;E. M. Lifshitz
  27. Introduction to Mechanics and Symmetry J. E. Marsden;T. S. Ratiu
  28. Ph. D. Thesis Bildgebung durch klinische Magnetresonanztomographie S. Pods
  29. Pitman Research Notes in Mathematics Series v.147 Harmonic Analysis on the Heisenberg Niloptent Lie Group with Applications to Signal Theotry W. J. Schempp
  30. Mathematical Foundations and Applicatipns Magnetic Resonance Imaging, Mathematical Foundations and Applications W. J. Schempp
  31. Applied Math. Sciencs v.30 Geometric Quantization and Quantum Mechanics J. Sniatycki
  32. arXiv:hep-th/9409089 v.2 The World as a hologram L. Susskind
  33. Weyl Transforma M. W. Wong