Functorial Differential Spaces and the Infinitesimal Structure of Space-Time

Leszek Pysiak , Wiesław Sasin , Michael Heller , Tomasz Miller

Abstract

We generalize the differential space concept as a tool for developing differential geometry, and enrich this geometry with infinitesimals that allow us to penetrate into the superfine structure of space. This is achieved by Yoneda embedding a ring of smooth functions into the category of loci. This permits us to define a category of functorial differential spaces. By suitably choosing various algebras as “stages” in this category, one obtains various classes of differential spaces, both known from the literature and many so far unknown. In particular, if one chooses a Weil algebra, infinitesimals are produced.
Author Leszek Pysiak (FMIS / DDG)
Leszek Pysiak,,
- Department of Differential Geometry
, Wiesław Sasin (FMIS / DDG)
Wiesław Sasin,,
- Department of Differential Geometry
, Michael Heller
Michael Heller,,
-
, Tomasz Miller (FMIS)
Tomasz Miller,,
- Faculty of Mathematics and Information Science
Journal seriesReports on Mathematical Physics, ISSN 0034-4877
Issue year2020
Vol85
No3
Pages443-454
Publication size in sheets0.55
Keywords in Polishfunktorialne przestrzenie różniczkowe
Keywords in Englishfunctorial differential spaces
ASJC Classification2610 Mathematical Physics; 3109 Statistical and Nonlinear Physics
Abstract in PolishArtykuł poświęcony jest teorii funktorialnych przestrzeni różniczkowych w obszarze geometrii syntetycznej z zastosowaniem do osobliwości początkowej w modelu Robertsona Walkera.
DOIDOI:10.1016/S0034-4877(20)30046-X
URL https://www.sciencedirect.com/science/article/pii/S003448772030046X#
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 14-07-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.7; WoS Impact Factor: 2018 = 0.989 (2) - 2018=0.848 (5)
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