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Bibliographic Details
Main Authors: zhou, changzheng, zhou, ziqing
Format: Recurso digital
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Published: Zenodo 2026
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Online Access:https://doi.org/10.5281/zenodo.19250876
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  • <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>