An Algebraic Foundation of Amended Dimensional Analysis
Mathematical Physics
2020-12-15 v2 math.MP
Rings and Algebras
Abstract
We present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory of quantity spaces. Examples of dimensional analysis based on this approach are given, showing that it allows results obtained by traditional dimensional analysis to be strengthened. For example, the orbital period of a two-body system can be derived without use of equations of motion.
Cite
@article{arxiv.2010.15769,
title = {An Algebraic Foundation of Amended Dimensional Analysis},
author = {Dan Jonsson},
journal= {arXiv preprint arXiv:2010.15769},
year = {2020}
}
Comments
18 pages, Theorem 2 added. Overlaps with and supersedes arXiv:2005.10645