Compositional Quantum Field Theory: An axiomatic presentation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914661693128704 |
|---|---|
| author | Oeckl, Robert Almada, Juan Orendain |
| author_facet | Oeckl, Robert Almada, Juan Orendain |
| contents | We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of Quantum Field Theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of General Boundary Quantum Field Theory, and is phrased in terms of correspondences between certain commuting diagrams of gluing identifications between manifolds and corresponding commuting diagrams of state-spaces and linear maps, thus making it amenable to formalization in terms of involutive symmetric monoidal functors and operad algebras. The underlying novel framework for gluing leads to equivariance of CQFT. We study CQFTs in dimension 2 and the algebraic structure they define on open and closed strings. We also consider, as a particular case, the compositional structure of 2-dimensional pure quantum Yang-Mills theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10385 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Compositional Quantum Field Theory: An axiomatic presentation Oeckl, Robert Almada, Juan Orendain High Energy Physics - Theory Mathematical Physics Category Theory We introduce Compositional Quantum Field Theory (CQFT) as an axiomatic model of Quantum Field Theory, based on the principles of locality and compositionality. Our model is a refinement of the axioms of General Boundary Quantum Field Theory, and is phrased in terms of correspondences between certain commuting diagrams of gluing identifications between manifolds and corresponding commuting diagrams of state-spaces and linear maps, thus making it amenable to formalization in terms of involutive symmetric monoidal functors and operad algebras. The underlying novel framework for gluing leads to equivariance of CQFT. We study CQFTs in dimension 2 and the algebraic structure they define on open and closed strings. We also consider, as a particular case, the compositional structure of 2-dimensional pure quantum Yang-Mills theory. |
| title | Compositional Quantum Field Theory: An axiomatic presentation |
| topic | High Energy Physics - Theory Mathematical Physics Category Theory |
| url | https://arxiv.org/abs/2208.10385 |