III. Algebraic Geometrical Aspects of Quantum InformationNo Access

QUANTUM THEORY AND GALOIS FIELDS

FELIX M. LEV

Artwork Conversion Software Inc., 1201 Morningside Drive, Manhattan Beach, CA 90266, USA

https://doi.org/10.1142/S0217979206034273Cited by:1 (Source: Crossref)

Abstract

We discuss the motivation and main results of a quantum theory over a Galois field (GFQT). The goal of the paper is to describe main ideas of GFQT in a simplest possible way and to give clear and simple arguments that GFQT is a more natural quantum theory than the standard one.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

S. Weinberg , Dreams of a Final Theory ( A Division of Random House Inc. , New York , 1992 ) . Google Scholar
S. Weinberg , Quantum Theory of Fields ( Cambridge University Press , Cambridge , 1995 ) . Crossref, Google Scholar
P. A. M. Dirac , Mathematical Foundations of Quantum Theory , ed. A. R. Marlow ( Academic Press , New York, San Francisco, London , 1978 ) . Crossref, Google Scholar
W. Pauli , Handbuch der Physik V/1 ( Berlin , 1958 ) . Google Scholar
Y. Aharonov and D. Bohm, Phys. Rev. 122, 1649 (1961), 134, 1417 (1964) . Google Scholar
V. A. Fock, ZhETF 42, 1135 (1962). Google Scholar
B. A. Lippman, Phys. Rev. 151, 1023 (1966). Crossref, Web of Science, Google Scholar
T. D. Newton and E. P. Wigner, Rev. Mod. Phys. 21, 400 (1949). Crossref, Web of Science, ADS, Google Scholar
V. B. Berestetsky , E. M. Lifshits and L. P. Pitaevsky , Relativistic Quantum Theory IV-1 ( Nauka , Moscow , 1968 ) . Google Scholar
L. Rosenfeld , N. Bohr and the Development of Physics , ed. W. Pauli ( Pergamon Press , London , 1955 ) . Google Scholar
C. Brans and R. H. Dicke, Phys. Rev. 124, 925 (1961). Crossref, Web of Science, ADS, Google Scholar
S. Weinberg , Gravitation and Cosmology ( John Wiley & Sons Inc. , 1972 ) . Google Scholar
S. Weinberg, "What is Quantum Field Theory, and What Did We Think It Is?", hep-th/9702027 . Google Scholar
E. P. Wigner, Ann. Math. 40, 149 (1939). Crossref, Web of Science, ADS, Google Scholar
T. Kato , Perturbation Theory for Linear Operators ( Springer-Verlag , Berlin - Heidelberg - New York , 1966 ) . Crossref, Google Scholar
P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949). Crossref, Web of Science, ADS, Google Scholar
B. L. Van der Waerden , Algebra I ( Springer-Verlag , Berlin - Heidelberg - New York , 1967 ) . Crossref, Google Scholar
K. Ireland and M. Rosen , A Classical Introduction to Modern Number Theory , Graduate Texts in Mathematics-87 ( Springer , New York - Heidelberg - Berlin , 1987 ) . Google Scholar
F. M. Lev, J. Math. Phys. 30, 1985 (1989); J. Math. Phys. 34, 490 (1993) . Google Scholar
F. Lev, "Why is Quantum Physics Based on Complex Numbers?", hep-th/0309003 (to be published in Finite Fields and Their Applications; the online version of the paper is available at www.sciencedirect.com) . Google Scholar
F. Lev, "Quantum Theory on a Galois Field", hep-th/0403231 . Google Scholar
Y. Nambu , Quantum Field Theory and Quantum Statistics , eds. I. A. Batalin et al. ( Adam Hilger , Bristol , 1987 ) . Google Scholar
A. Vourdas, Rep. Progr. Phys. 67, 267 (2004). Crossref, Web of Science, ADS, Google Scholar
H. Doughty, Private Communication of June 24th, 2004 . Google Scholar
M. Planat and M. Saniga, Endophysics, Time, Quantum and the Subjective, eds. R. Buccheri, A. C. Elitzur and M. Saniga (World Scientific, Singapore, 2005) pp. 409–426. Link, Google Scholar
M. Planat, "Huyghens, Bohr, Riemann and Galois: Phase-Locking", math-ph/0510044 (to be published in Int. J. Mod. Phys. B) . Google Scholar
M. Planat and H. Rosu, Eur. Phys. J. D. 36, 133 (2005). Crossref, Web of Science, ADS, Google Scholar
E. Inonu and E. P. Wigner, Nuovo Cimento IX, 705 (1952). Google Scholar
P. J. E. Peebles and B. Ratra, Rev. Mod. Phys. 75, 559 (2003). Crossref, Web of Science, ADS, Google Scholar
J. Polchinski, "M Theory: Uncertainty and Unification", hep-th/0209105 . Google Scholar
M. Flato and C. Fronsdal, Lett. Math. Phys. 2, 421 (1978). Crossref, Web of Science, ADS, Google Scholar
L. Castell and W. Heidenreich, Phys. Rev. D 24, 371 (1981). Crossref, Web of Science, ADS, Google Scholar
F. M. Lev, Theor. Math. Phys. 138, 208 (2004); J. Phys. A37, 3285 (2004) . Google Scholar
E. P. Wigner , The World Treasury of Physics, Astronomy and Mathematics , ed. Timothy Ferris ( Little Brown and Company , Boston-New York-London , 1991 ) . Google Scholar