Expansão em derivadas da ação efetiva de 1-loop

Abstract

In this dissertation, the derivative expansion of the effective action is analyzed in a field theory with two interacting real scalar fields in curved spacetime. A functional approach is adopted to determine the effective action in flat space, and using the local momentum representation, it is possible to generalize the result to curved space. Initially, the coefficient of the kinetic term is computed in the case of a single scalar field, including corrections up to first order in curvature. Subsequently, the two-field problem is treated through a double diagonalization procedure, which allows for the diagonalization of the Hessian matrix and the reduction to the case of a single scalar with an effective mass. Furthermore, the case with a mass hierarchy is considered, showing that both the renormalized effective potential and the coefficients of the derivative terms exhibit quantum decoupling, confirming the validity of the effective theory in the low-energy regime. The original results of this dissertation were published in the article "Derivative expansion in a two-scalar field theory" by Alícia G. Borges and Ilya L. Shapiro, in the journal Physical Review D on June 25, 2025 (DOI: 10.1103/rynr-2znv). These results were also presented by Alícia G. Borges at the scientific events “Quantum Summer 2025” (PPG-Cosmo, UFES), “As Astrocientistas: III Brazilian Meeting of Girls and Women in Astrophysics, Gravitation and Cosmology” (PPG-Cosmo, UFES; CBPF), and “School of Cosmology and Gravitation” (CBPF).