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Feynman Diagrams beyond Physics: From Biology to Economy

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  • Nicolò Cangiotti

    (Department of Mathematics, Politecnico di Milano, Via Bonardi 9, Edificio 14 “Nave”, Campus Leonardo, 20133 Milan, Italy)

Abstract

Feynman diagrams represent one of the most powerful and fascinating tools developed in theoretical physics in the last century. Introduced within the framework of quantum electrodynamics as a suitable method for computing the amplitude of a physical process, they rapidly became a fundamental mathematical object in quantum field theory. However, their abstract nature seems to suggest a wider usage, which actually exceeds the physical context. Indeed, as mathematical objects, they could simply be considered graphs that depict not only physical quantities but also biological or economic entities. We survey the analytical and algebraic properties of such diagrams to understand their utility in several areas of science, eventually providing some examples of recent applications.

Suggested Citation

  • Nicolò Cangiotti, 2024. "Feynman Diagrams beyond Physics: From Biology to Economy," Mathematics, MDPI, vol. 12(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1295-:d:1382346
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    References listed on IDEAS

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    1. Bagarello, F., 2007. "Stock markets and quantum dynamics: A second quantized description," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 283-302.
    2. Belal E. Baaquie, 2005. "A Common Market Measure For Libor And Pricing Caps, Floors And Swaps In A Field Theory Of Forward Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 999-1018.
    3. Bon, M. & Orland, H., 2010. "Prediction of RNA secondary structures with pseudoknots," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(15), pages 2987-2992.
    4. Giovanni Paolinelli & Gianni Arioli, 2018. "A path integral based model for stocks and order dynamics," Papers 1803.07904, arXiv.org.
    5. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    6. Baaquie, Belal E., 2006. "Price of coupon bond options in a quantum field theory of forward interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 98-103.
    7. Giovanni Paolinelli & Gianni Arioli, 2018. "A model for stocks dynamics based on a non-Gaussian path integral," Papers 1809.01342, arXiv.org, revised Oct 2018.
    8. Belal E. Baaquie, 2005. "A Common Market Measure for Libor and Pricing Caps, Floors and Swaps in a Field Theory of Forward Interest Rates," Papers physics/0503126, arXiv.org.
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