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Titolo: Physical equivalence on nonstandard spaces and symmetries on infinitesimallattice spaces
Autore: Kobayashi, T;
 Indirizzi:
 Tsukuba Coll Technol, Dept Gen Educ, Tsukuba, Ibaraki 3050005, Japan Tsukuba Coll Technol Tsukuba Ibaraki Japan 3050005 Ibaraki 3050005, Japan
 Titolo Testata:
 NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA BGENERAL PHYSICS RELATIVITY ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS
fascicolo: 4,
volume: 116,
anno: 2001,
pagine: 403  426
 SICI:
 11241888(200104)116:4<403:PEONSA>2.0.ZU;2B
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 DECOHERENCE; MOTIONS; STATES;
 Tipo documento:
 Article
 Natura:
 Periodico
 Settore Disciplinare:
 Physical, Chemical & Earth Sciences
 Citazioni:
 15
 Recensione:
 Indirizzi per estratti:
 Indirizzo: Kobayashi, T Tsukuba Coll Technol, Dept Gen Educ, Tsukuba, Ibaraki 3050005, Japan Tsukuba Coll Technol Tsukuba Ibaraki Japan 3050005 05, Japan



 Citazione:
 T. Kobayashi, "Physical equivalence on nonstandard spaces and symmetries on infinitesimallattice spaces", NUOV CIM B, 116(4), 2001, pp. 403426
Abstract
Equivalence in physics is discussed on the basis of experimental data accompanied by experimental errors. The introduction of the equivalence being consistent with the mathematical definition is possible only in theories constructed on nonstandard number spaces by taking the experimental errors asinfinitesimal numbers of the nonstandard spaces. Following the idea for the equivalence (the physical equivalence), a new description of spacetime in terms of infinitesimallattice points on the nonstandard real number space *R is proposed. The infinitesimallattice space, *L, is represented by the set of points on *R which are written by l(n) = n*epsilon, where the infinitesimal lattice spacing *epsilon is determined by a, nonstandard natural number *N such that *epsilon equivalent to *N1. By using infinitesimal neighborhoods (Mon(r \ *L)) of a real number r on *L, we can make a space *M which is isomorphic to R as additive group. Therefore, every point on (*M)(N) automatically has the internal confinedsubspace Mon(r \ *L). A field theory on *L is proposed. To determine a projection from *L to *M, a fundamental principle based on the physical equivalence is introduced. The physical equivalence is expressed by the totally equal treatment for indistinguishable quantities in our observations. Following the principle, we show thatthe U(I) and SU(N) symmetries on the space (*M)(N) are induced from the internal substructure (Mon(r \ *L))(N). A quantized state describing the configuration space is constructed on (*M)(N). By providing that the subspace (Mon(r \ *L))(N) is a local inertial system of general relativity, infinitesimal distance operators are consistently introduced. We see that Lorentz and general relativistic transformations are also represented by operators which involve the U(l) and SU(N) internal symmetries.
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Documento generato il 31/03/20 alle ore 15:34:44