排序方式: 共有31条查询结果,搜索用时 15 毫秒
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Elias Zafiris 《International Journal of Theoretical Physics》2004,43(1):265-298
We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime. 相似文献
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Jerzy Król 《Foundations of Physics》2006,36(7):1070-1098
We analyse the proposition that the spacetime structure is modified at short distances or at high energies due to weakening of classical logic. The logic assigned to the regions of spacetime is intuitionistic logic of some topoi. Several cases of special topoi are considered. The quantum mechanical effects can be generated by such semi-classical spacetimes. The issues of: background independence and general relativity covariance, field theoretic renormalization of divergent expressions, the existence and definition of path integral measures, are briefly discussed in the proposal. The connection with some problems in foundations of mathematics and differential topology are also discussed. 相似文献
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Warren Dicks 《Journal of Pure and Applied Algebra》1983,27(1):15-28
Let λ be a finitary geometric theory and δ its classifying topos. We prove that δ is Boolean if and only if (1) every first-order formula in the language of λ is ?-provably equivalent to a geometric formula and (2) for any finite list of varibles, x, there are, up to ?-provable equivalence, only finitely many formulas, in the language of λ with free variables among x. We use this characterization to show that, when δ is Boolean, it is an atomic topos and can be viewed as a finite coproduct of topoi of continuous G-sets for topological groups G satisfying a certain finiteness condition. 相似文献
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Tibor Beke 《K-Theory》2004,32(4):293-322
We introduce a notion of cover of level n for a topological space, or more generally any Grothendieck site, with the key property that simplicial homotopy classes computed along the filtered diagram of n-covers biject with global homotopy classes when the target is an n-type. When the target is an Eilenberg–MacLane sheaf, this specializes to computing derived functor cohomology, up to degree n, via simplicial homotopy classes taken along n-covers. Our approach is purely simplicial and combinatorial. 相似文献
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Giovanni Curi 《Mathematical Logic Quarterly》2010,56(4):375-387
This paper presents several independence results concerning the topos‐valid and the intuitionistic (generalised) predicative theory of locales. In particular, certain consequences of the consistency of a general form of Troelstra's uniformity principle with constructive set theory and type theory are examined (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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