2020/10/29 by Dan Jönsson, Jonsson, Dan
Computer Science · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Quantum chaos and dynamical systems #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2010.15769
openalex publication_date 2020/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.