2005/05/16 by Elemér E Rosinger, Elemer E Rosinger, Rosinger, Elemer E · 2 citations
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #History and Overview (math.HO) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.HO #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.math/0505336
arxiv created 2005/05/16 · openalex publication_date 2005/05/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are compelling historical and mathematical reasons why we ended up, among others in Physics, with using the scalars given by the real or the complex numbers. Recently, however, infinitely many easy to construct and use other algebras of scalars have quite naturally emerged in a number of branches of Applied Mathematics. These algebras of scalars can deal with the long disturbing difficulties encountered in Physics, related to such phenomena as "infinities in Physics", "re-normalization", the "Feynman path integral", and so on. Specifically, as soon as one is dealing with scalars in algebras which - unlike the reals R and complex numbers C - are no longer Archimedean, one can deal with a large variety of "infinite" quantities and do so within the usual rules and with the usual operations of algebra. Here we present typical constructions of these recently emerged algebras of scalars, most of them non-Archimedean.