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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.53 supl.1 Bogotá Dec. 2019 Epub Mar 24, 2020
https://doi.org/10.15446/recolma.v53nsupl.84010
Artículos originales
Renormalisation via locality morphisms
1 University of Potsdam, Germany
This is a survey on renormalisation in algebraic locality setup highlighting the role that locality morphisms can play for renormalisation purposes. After describing the general framework to build locality regularisation maps, we illustrate renormalisation by locality algebra homomorphisms on three examples, the renormalisation of conical zeta functions at poles, the definition of branched zeta functions and their evaluation at poles and finally the values of iterated integrals stemming from Kreimer's toy model.
Keywords: locality; renormalisation; partial algebra; operated algebra; Hopf algebra; Rota-Baxter algebra; symbols
Éste es un estudio sobre la renormalización en la configuración de la localidad algebraica, que resalta el papel que los morfismos de la localidad pueden desempeñar para los propósitos de la renormalización. Después de describir el marco general para construir mapas de regularización de la localidad, ilustramos la renormalización mediante homomorfismos de álgebras de la localidad en tres ejemplos, la renormalización de las funciones zeta cónica en los polos, la definición de las funciones zeta ramificadas y su evaluación en los polos y, finalmente, los valores de las integrales iteradas derivadas del modelo de juguete de Kreimer.
Palabras clave: localidad; renormalización; álgebra parcial; álgebra operada; álgebra de Hopf; álgebra de Rota-Baxter; símbolos
REFERENCES
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Received: October 13, 2018; Accepted: March 11, 2019
Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons BY
