Iterant Algebra
We give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use this point of view to discuss the Schrödinger and Di...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/7/347 |
| _version_ | 1818040359392903168 |
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| author | Louis H. Kauffman |
| author_facet | Louis H. Kauffman |
| author_sort | Louis H. Kauffman |
| collection | DOAJ |
| description | We give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use this point of view to discuss the Schrödinger and Dirac equations, Majorana Fermions, representations of the braid group and the framed braids in relation to the structure of the Standard Model for physics. |
| first_indexed | 2024-12-10T08:13:16Z |
| format | Article |
| id | doaj.art-353d43c41f814ca2827e451cc46c1b23 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-12-10T08:13:16Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-353d43c41f814ca2827e451cc46c1b232022-12-22T01:56:31ZengMDPI AGEntropy1099-43002017-07-0119734710.3390/e19070347e19070347Iterant AlgebraLouis H. Kauffman0Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045, USAWe give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use this point of view to discuss the Schrödinger and Dirac equations, Majorana Fermions, representations of the braid group and the framed braids in relation to the structure of the Standard Model for physics.https://www.mdpi.com/1099-4300/19/7/347iterantClifford algebramatrix algebrabraid groupFermionDirac equation |
| spellingShingle | Louis H. Kauffman Iterant Algebra Entropy iterant Clifford algebra matrix algebra braid group Fermion Dirac equation |
| title | Iterant Algebra |
| title_full | Iterant Algebra |
| title_fullStr | Iterant Algebra |
| title_full_unstemmed | Iterant Algebra |
| title_short | Iterant Algebra |
| title_sort | iterant algebra |
| topic | iterant Clifford algebra matrix algebra braid group Fermion Dirac equation |
| url | https://www.mdpi.com/1099-4300/19/7/347 |
| work_keys_str_mv | AT louishkauffman iterantalgebra |