Μελέτη κβαντικών θεωριών πεδίου σε πεπερασμένη θερμοκρασία

Abstract

In this dissertation, ?eld theories at ?nite temperature are studied. The techniques needed for this study, enable the user to develop calculational skills for treating ?eld theo- ries with compact dimensions. So conceptually and from a calculational point of view the two seem to be equivalent. So following this line, we develop all the necessary formalism of ?nite temperature ?eld theories and then apply it to supersymmetric ?eld theories. Also the construction of supersymmetric models of various supersymmetry represetations is described. Speci?cally we study supersymmetry breaking at ?nite temperature. It is known that it breaks spontaneously, so we examine supersymmetry breaking for models with a compact dimension. The study is focused for an N = 1 supersymmetric model in a S1£R3 spacetime. We ?nd that by choosing appropriate boundary conditions for the contributing ?elds supersymmetry can be preserved. However if we add a hard supersym- metry breaking term, we observe that for small values of the length of the S1 dimension, supersymmetry remains unbroken and breaks spontaneously when the length exceeds a critical value. The ?nal picture resembles the ?rst order phase transition picture. A toy cosmological application is discussed. In another application of both the ?nite temper- ature formalism and the formalism of ?eld theories with compact dimensions, we study the temperature inversion symmetry, for a non interacting supersymmetric ensemble (free twisted Wess-Zumino model), at ?nite volume. It is found that, the scaled free energy, f(»), is antisymmetric under temperature inversion transformation, i.e. f(») = ?»df( 1 » ). This occurs for antiperiodic bosons and periodic fermions, in the compact dimension. On the contrary, for periodic bosons and antiperiodic fermions, f(») = »df( 1 » ). As a ?nal application we generalize the study of the temperature inversion symmetry R ! 1 T for the ?nite temperature e®ective potential of two supersymmetric, d = 5 gauge-Higgs u- ni?cation models with Scherk-Schwarz supersymmetry breaking. The N = 1, d = 5, SU(3)c£SU(3)w model, on the orbifold S1=Z2 is studied ?rst. For the value of the Wilson line parameter ® = 1 (SU(2)L breaks to a U0(1)), it is found that the e®ective potential contains a symmetric part and an anti-symmetric part under » ! 1 » , with, » = RT. When ® = 0 (for which, SU(2)L remains unbroken) it is found that the only contribution to the e®ective potential that spoils the temperature inversion symmetry comes from the fermions in the fundamental representation of the gauge group, with (+; +) or (?;?), Z2 parities. This is of particular importance since it implies that models with orbifold ?xed point localized fundamental fermions (and with no bulk fundamental fermions) have the temperature inversion symmetry. The case of N = 1, d = 5, SU(5) is brie°y discussed in the end.