An algebraic approach to physical scales

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Authors	JANYŠKA Josef MODUGNO Marco VITOLO Raffaele
Year of publication	2010
Type	Article in Periodical
Magazine / Source	Acta Applicandae Mathematicae
MU Faculty or unit	Faculty of Science
Citation
Web	http://www.springerlink.com/content/100230/?Content+Status=Accepted&sort=p_OnlineDate&sortorder=desc&v=condensed
Field	Theoretical physics
Keywords	semi-vector spaces; scales; units of measurement
Description	This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved by means of the concept of ``positive space" and its rational powers. Positive spaces are ``semi--vector spaces'' on which the group of positive real numbers acts freely and transitively through the scalar multiplication. Their tensor multiplication with vector spaces yields ``scaled spaces'' that are suitable to describe spaces with physical dimensions mathematically. We also deal with scales regarded as fields over a given background e.g., spacetime.
Related projects:	Mathematical structures and their physical applications Geometric structures on fibered manifolds