Subadditivity and additivity of the Yang-Mills action functional in Noncommutative Geometry
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2017
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917205793308672 |
|---|---|
| author | Guin, Satyajit |
| author_facet | Guin, Satyajit |
| contents | We formulate notions of subadditivity and additivity of the Yang-Mills action functional in noncommutative geometry. We identify a suitable hypothesis on spectral triples which proves that the Yang-Mills functional is always subadditive, as per expectation. The additivity property is much stronger in the sense that it implies the subadditivity property. Under this hypothesis we obtain a necessary and sufficient condition for the additivity of the Yang-Mills functional. An instance of additivity is shown for the case of noncommutative $n$-tori. We also investigate the behaviour of critical points of the Yang-Mills functional under additivity. At the end we discuss few examples involving compact spin manifolds, matrix algebras, noncommutative $n$-torus and the quantum Heisenberg manifolds which validate our hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_00986 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Subadditivity and additivity of the Yang-Mills action functional in Noncommutative Geometry Guin, Satyajit Operator Algebras Mathematical Physics 58B34, 81T75 We formulate notions of subadditivity and additivity of the Yang-Mills action functional in noncommutative geometry. We identify a suitable hypothesis on spectral triples which proves that the Yang-Mills functional is always subadditive, as per expectation. The additivity property is much stronger in the sense that it implies the subadditivity property. Under this hypothesis we obtain a necessary and sufficient condition for the additivity of the Yang-Mills functional. An instance of additivity is shown for the case of noncommutative $n$-tori. We also investigate the behaviour of critical points of the Yang-Mills functional under additivity. At the end we discuss few examples involving compact spin manifolds, matrix algebras, noncommutative $n$-torus and the quantum Heisenberg manifolds which validate our hypothesis. |
| title | Subadditivity and additivity of the Yang-Mills action functional in Noncommutative Geometry |
| topic | Operator Algebras Mathematical Physics 58B34, 81T75 |
| url | https://arxiv.org/abs/1712.00986 |