Ramírez Romero, CupatitzioCartas Fuentevilla, RobertoRAMIREZ ROMERO, CUPATITZIO; 10825CARTAS FUENTEVILLA, ROBERTO; 16034Cruz Limón, Oscar2025-04-092025-04-092024-12https://hdl.handle.net/20.500.12371/27494"This thesis develops a field theory for dissipative systems, employing a hypercomplex ring formalism that naturally reproduces dissipative systems’ effective doubling field formulation in the context of thermal field theory. The system is defined by a non-canonical ansatz that ensures the conservation of unitarity. Asymptotically entangled states are developed to facilitate the analysis of ergodicity in systems experiencing entanglement. In addition, calculations of partition functions in a hyperbolic ring and a hypercomplex ring are performed. A significant part of this thesis is based on the reference. The results shown in this thesis have already been published. The development of the present work follows the steps outlined in, but introduces an extension of the formalism. The section devoted to the partition function in a pure hyperbolic ring in chapter 5 of this work represents an extension of the research presented in. As for the partition function in the hypercomplex ring in chapter 6, this is unpublished content that is currently in the process of publication".pdfengCIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRAMatemáticas--Álgebra--Números complejosMatemáticas--Álgebra--Anillos y álgebras no conmutativasFísica--Física matemática--Temas especiales--Sistemas hamiltonianosFísica--Física atómica--Teoría cuántica--Teoría cuántica de camposTesis de doctoradoopenAccess