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Janyška, Josef; Modugno, Marco; Vitolo, Raffaele

An algebraic approach to physical scales. (English) Zbl 1208.15021

Acta Appl. Math. 110, No. 3, 1249-1276 (2010).
The authors propose the category of positive spaces (i.e. essentially the \(1\)-dimensional semi-vector spaces over \(\mathbb R^{+}\)) and \(q\)-rational maps (for all \(q \in Q\)) between them, as a convenient mathematical setting to formulate the intuitive notions of physical scales and units of measurement. To this end, semi-tensor products, spaces of morphisms and rational powers of a positive space are treated. Besides, using methods of Differential Geometry, the bundles of positive spaces based on spacetime and their semi-linear connections are discussed. A brief review of the relationship to dimensional analysis is also given [e.g., see G. I. Barenblatt, Scaling. Cambridge Texts in Applied Mathematics. Cambridge: Cambridge University Press (2003; Zbl 1094.00006)].
Reviewer: George F. Nassopoulos (Athens)

Cited in 1 Review
Cited in 14 Documents

MSC:

15A69 Multilinear algebra, tensor calculus
12K10 Semifields
16Y60 Semirings
70S99 Classical field theories

Keywords:

semi-vector spaces; scales; units of measurement; \(q\)-rational maps; semi-tensor products; spaces of morphisms; bundles of positive spaces; semi-linear connections

Citations:

Zbl 1094.00006
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Full Text: DOI

References:

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