Mantiñan, Matías N. (2021) Teoria de campos de backgrounds no triviales: efectos semiclásicos / Quantum field theory in non-trivial backgrounds: semiclassical effects. Maestría en Ciencias Físicas, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En este trabajo se estudiaron distintos aspectos de las teorías de campos en fondos no triviales, teniendo como objetivo el análisis del efecto Casimir en presencia de medios no homogéneos, con la mirada puesta en el estudio de las divergencias que la teoría presenta en medios discontinuos y en la validez del llamado principio de trabajos virtuales. Se utilizó un campo escalar con masa variable como modelo simplificado para el estudio de las fluctuaciones del vacío del campo electromagnético en presencia de medios no homogéneos, con la masa jugando el papel de la permeabilidad/permitividad. Utilizando técnicas de la teoría cuántica de campos en espacios curvos, se obtuvieron las divergencias esperadas para los valores medios ⟨ϕ"2⟩ y ⟨T_μν⟩ en la teoría escalar. Se calcularon estos valores medios perturbativamente en potencias de la masa. Se obtuvieron expresiones formales válidas a todo orden y luego se estudiaron en detalle el primer y segundo orden del desarrollo. Se aislaron las divergencias obtenidas por regularización dimensional y se evaluaron las partes finitas. Con el desarrollo para ⟨T_μν⟩ se obtuvo la energía orden a orden, y se calculó la fuerza entre regiones con distinta masa al orden más bajo no trivial. La fuerza se obtuvo como la derivada de la energía respecto a la posición de los cuerpos interactuantes, y la consistencia de este resultado con la presión sobre los cuerpos debido al campo es lo que en la bibliografía se conoce como principio de trabajos virtuales. Se demostró el principio de trabajos virtuales para una configuración general y a todo orden para esta teoría. Finalmente se reobtuvieron algunos resultados utilizando el formalismo de la acción efectiva, y se mostró como generalizarlos al caso en que los backgrounds dependen del tiempo. En este caso, se vuelve imprescindible utilizar el formalismo de Schwinger-Keldysh o de camino temporal cerrado.
Resumen en inglés
In this work, we studied different aspects of Quantum Field Theories in non-trivial backgrounds, where we intend to analyse the Casimir Effect in inhomogeneous media. Throughout this thesis, we had an eye on the study of divergences appearing in theories presenting discontinuous media, and the validity of the so-called Principle of Virtual Works. We used a scalar field with a variable mass as a simple model for the study of the vacuum fluctuations of the electromagnetic field in inhomogeneous media, with the mass playing the role of permeability/permittivity. Using techniques of Quantum Field Theory in Curved Spacetimes, we obtained the divergences of the mean values ⟨ϕ"2⟩ and ⟨T_µν⟩ for the scalar theory. We did the calculations of these mean values perturbatively, in powers of the mass, and obtained formal expressions valid up to every order. Afterwards, we studied in detail the first two terms of the expansion. Furthermore, we isolated the divergences obtained under dimensional regularization, and we evaluated the finite parts. Using the expansion of ⟨T_µν⟩, we obtained the energy up to every order, and we did the calculation of the force between regions with different masses up to the first non-trivial order. We obtained the force as the derivative of the energy with respect to the position of the interacting bodies. The consistency of this result is what is known in the bibliography as the Principle of Virtual Works. We proved the Principle of Virtual Works for a general configuration and to every order for the scalar theory we studied. Finally, we reobtained some results using the formalism of the Effective Action, and we showed how to generalize the results to the case where the background depends on the time. In that case, one must use the Schwinger-Keldysh formalism, also known as Closed Time Path formalism.
| Tipo de objeto: | Tesis (Maestría en Ciencias Físicas) |
|---|---|
| Palabras Clave: | Quantum field theory, Teoría del campo cuántico; Casimir effect; Efecto casimir; Renormalization; Renormalización; [Principle of virtual work; Principio de trabajos virtuales] |
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| Materias: | Física > Teoría de campos |
| Divisiones: | Investigación y aplicaciones no nucleares > Física > Partículas y campos |
| Código ID: | 1054 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 08 Jul 2022 15:01 |
| Última Modificación: | 08 Jul 2022 15:01 |
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