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Titolo:
Physical equivalence on non-standard spaces and symmetries on infinitesimal-lattice 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 B-GENERAL PHYSICS RELATIVITY ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS
fascicolo: 4, volume: 116, anno: 2001,
pagine: 403 - 426
SICI:
1124-1888(200104)116:4<403:PEONSA>2.0.ZU;2-B
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 non-standard spaces and symmetries on infinitesimal-lattice spaces", NUOV CIM B, 116(4), 2001, pp. 403-426

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 non-standard number spaces by taking the experimental errors asinfinitesimal numbers of the non-standard spaces. Following the idea for the equivalence (the physical equivalence), a new description of space-time in terms of infinitesimal-lattice points on the non-standard real number space *R is proposed. The infinitesimal-lattice 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, non-standard natural number *N such that *epsilon equivalent to *N-1. 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 confined-subspace 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