| _version_ | 1866901359294414848 |
|---|---|
| author | zhou, changzheng zhou, ziqing |
| author_facet | zhou, changzheng zhou, ziqing |
| contents | <p>This paper establishes a correspondence between generative categories and the<br>mathematical structures of quantum field theory, reinterpreting the operator al<br>gebra in quantum field theory as a linearized version of generative categories. By<br>aligning the combinatorial rules of Feynman diagrams with the composition of mor<br>phisms in generative categories, it is shown that the duality of diagrams corresponds<br>to the duality of categories. On this basis, a correspondence between generative cat<br>egories and tensor categories is established, where the tensor product is interpreted<br>as the parallel composition of generative processes. A key theorem demonstrates<br>that a generative system satisfying information conservation automatically pos<br>sesses a rigid structure, thereby forming a tensor category, whose Grothendieck<br>ring corresponds to the fusion ring in physics. As an application, the Verlinde for<br>mula in conformal field theory is reinterpreted as a duality condition for generative<br>categories, with the central charge corresponding to the dimension of the category.<br>Through a concrete construction of the SU(2)k Wess-Zumino-Witten model, the<br>consistency of the generative category framework with known results in conformal<br>field theory is verified, proving the operability of the correspondence established in<br>previous chapters.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19250876 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Generative Category Theory G: Physical Realization of Generative Categories zhou, changzheng zhou, ziqing Generative Categories; Tensor Categories; Quantum Field Theory; Feynman Diagrams; Verlinde Formula; Conformal Field Theory <p>This paper establishes a correspondence between generative categories and the<br>mathematical structures of quantum field theory, reinterpreting the operator al<br>gebra in quantum field theory as a linearized version of generative categories. By<br>aligning the combinatorial rules of Feynman diagrams with the composition of mor<br>phisms in generative categories, it is shown that the duality of diagrams corresponds<br>to the duality of categories. On this basis, a correspondence between generative cat<br>egories and tensor categories is established, where the tensor product is interpreted<br>as the parallel composition of generative processes. A key theorem demonstrates<br>that a generative system satisfying information conservation automatically pos<br>sesses a rigid structure, thereby forming a tensor category, whose Grothendieck<br>ring corresponds to the fusion ring in physics. As an application, the Verlinde for<br>mula in conformal field theory is reinterpreted as a duality condition for generative<br>categories, with the central charge corresponding to the dimension of the category.<br>Through a concrete construction of the SU(2)k Wess-Zumino-Witten model, the<br>consistency of the generative category framework with known results in conformal<br>field theory is verified, proving the operability of the correspondence established in<br>previous chapters.</p> |
| title | Generative Category Theory G: Physical Realization of Generative Categories |
| topic | Generative Categories; Tensor Categories; Quantum Field Theory; Feynman Diagrams; Verlinde Formula; Conformal Field Theory |
| url | https://doi.org/10.5281/zenodo.19250876 |