# Species-Theoretic Foundations of Perturbative Quantum Field Theory

@article{Norledge2020SpeciesTheoreticFO, title={Species-Theoretic Foundations of Perturbative Quantum Field Theory}, author={William Norledge}, journal={arXiv: Mathematical Physics}, year={2020} }

We develop an algebraic formalism for perturbative (local) quantum field theory (pQFT) which is based on Joyal's combinatorial species. We show that certain fundamental structures of pQFT are correctly viewed as algebraic structures internal to species. Aspects of this formalism have appeared in the physics literature, particularly in the work of Bogoliubov-Shirkov, Steinmann, Ruelle, and Epstein-Glaser-Stora. In this paper, we give a fully explicit account in terms of Aguiar-Mahajan's modern…

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