Renormalización mejorada y multipolos armónicos
Fecha
2023
Tipo
tesis de maestría
Autores
Solís Rodríguez, José Daniel
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Resumen
En este trabajo se proporciona una prueba de la estructura multipolar de los propagadores cinemáticos no regularizados de intensidades de campo de espín superior. Siguiendo el patrón identificado por primera vez en el trabajo original de Várilly y Gracia-Bondía, estos propagadores resultan ser multipolos armónicos en el sentido de Minkowski. En virtud de la noción refinada de Stora de una amplitud divergente y el principio de covarianza que sirve como base, se concluye que tales amplitudes
son regularizables mediante extensiones homogéneas únicas, las cuales transforman bajo la misma representación del grupo de Lorentz que sus campos cuánticos. Con la intención de explorar los límites de la dualidad entre las configuraciones euclidiana y minkowskiana en QFT, se establece un no-go theorem para la regularización de los propagadores de las intensidades de campo de espín superior.
A proof of the multipolar structure of the unregularized kinematic propagators of higher spin field strengths is provided. These follow the pattern identified first in the pioneering work of Varilly and Gracia-Bondía, meaning that the propagators are also harmonic multipoles, in the Minkowskian sense. By virtue of Stora’s refined notion of divergent amplitudes, and the guiding principle of covariance that serves as its bedrock, it can be concluded that all such amplitudes are regularizable by unique homogeneous extensions, transforming under the same representation of the Lorentz group as their quantum fields. In an attempt to explore the limits of the duality between the Euclidean and Minkowskian settings in QFT, a no-go theorem for the regularization of the higher spin field-strength propagators is established.
A proof of the multipolar structure of the unregularized kinematic propagators of higher spin field strengths is provided. These follow the pattern identified first in the pioneering work of Varilly and Gracia-Bondía, meaning that the propagators are also harmonic multipoles, in the Minkowskian sense. By virtue of Stora’s refined notion of divergent amplitudes, and the guiding principle of covariance that serves as its bedrock, it can be concluded that all such amplitudes are regularizable by unique homogeneous extensions, transforming under the same representation of the Lorentz group as their quantum fields. In an attempt to explore the limits of the duality between the Euclidean and Minkowskian settings in QFT, a no-go theorem for the regularization of the higher spin field-strength propagators is established.
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Palabras clave
NORMALIZACIÓN, RENORMALIZACIÓN, VALOR PRINCIPAL, MULTIPOLOS, FÍSICA