An algebraic approach to physical scales
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | Acta Applicandae Mathematicae |
| MU Faculty or unit | |
| 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. |
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