2023-Sustainable Industrial Processing Summit
SIPS2023 Volume 13. Intl. Symp on Physics, Mathematics and Multiscale Mechanics
| Editors: | F. Kongoli, A. B. Bhattacharya, A.C. Pandey, G. Sandhu, F. Quattrocchi, L. Sajo-Bohus, S. Singh, H.S. Virk, R.M. Santilli, M. Mikalajunas, E. Aifantis, T. Vougiouklis, P. Mandell, E. Suhir, D. Bammann, J. Baumgardner, M. Horstemeyer, N. Morgan, R. Prabhu, A. Rajendran |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2023 |
| Pages: | 298 pages |
| ISBN: | 978-1-989820-96-4 (CD) |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
CD shopping page
AN AXIOMATIC APPROACH TO THE INTERACTION CONCEPT IN PHYSICS
Jesus Cruz Guzman1;1UNIVERSIDAD NACIONAL AUTONOMA DE MEXICO, Coyoacan, Mexico;
Type of Paper: Regular
Id Paper: 387
Topic: 38
Abstract:
Using the category theory approach, we start defining a class of objects that is the class of bodies in a state of equilibrium. Interaction is the set of morphisms between objects in the category. The action $I_{01}$ (a morphism) of an external body $varPhi_1$ on the body $varPhi_0$ generate internal process $I_{0}$ (an automorphism). A set of automorphisms are related with the ``natural'' tendency of the body to evolve to a new equilibrium state that came's the measure of some property in $varPhi_1$. The notion of equilibrium is central and based on a dual relationship between two opposite categories. An equilibrium state is described by a set of scalar fields related with the observation process or during a modelling process. Then the system is described by an algebra over a field $F$, an $F-albebra$. Intensive and extensive physical properties and observer algebras are studied and some applications of the theory are discussed.
Keywords:
Mathematics; Physics; Interaction; Category TheoryReferences:
[1] Frank W. Anderson and Kent R. Fuller. Rings and Categories of Modules, volume 13 of Graduate Texts in Mathematics. Springer New York, 1974[2] Ole Immanuel Franksen. The nature of data—from measurements to systems. BIT, 25(1):24–50, jun 1985.
[3] A. Frolicher and A. Nijenhuis. Theory of vector valued differential forms. part i. derivations of the graded ring of differential forms. Indagat. Math., 18:338–359, 1956.
[4] Jose Bernabeu. Symmetries and their breaking in the fundamental laws of physics. Symmetry, 12(8), 2020.
[5] Saunders Mac Lane. Categories for the Working Mathematician, Graduate Texts in Mathematics 5, volume 5. Springer Science+Business Media, LLC, second edition edition, 1978.
[6] David M. Goodmanson. A graphical representation of the dirac algebra. Amer- ican Journal of Physics, 64:870–880, 7 1996.