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https://repositorio.ufba.br/handle/ri/5445
metadata.dc.type: | Artigo de Periódico |
Title: | Quantum fields in toroidal topology |
Other Titles: | Annals of Physics |
Authors: | Santana, Ademir Eugênio de Malbouisson, Jorge Mário Carvalho Malbouisson, Adolfo Pedro Carvalho Khanna, Faqir C. |
metadata.dc.creator: | Santana, Ademir Eugênio de Malbouisson, Jorge Mário Carvalho Malbouisson, Adolfo Pedro Carvalho Khanna, Faqir C. |
Abstract: | The standard representation of c∗-algebra is used to describe fields in compactified space–time dimensions characterized by topologies of the type Γ d D = (S1)d × MD−d. The modular operator is generalized to introduce representations of isometry groups. The Poincaré symmetry is analyzed and then we construct the modular representation by using linear transformations in the field modes, similar to the Bogoliubov transformation. This provides a mechanism for compactification of the Minkowski space–time, which follows as a generalization of the Fourier integral representation of the propagator at finite temperature. An important result is that the 2 × 2 representation of the real-time formalism is not needed. The end result on calculating observables is described as a condensate in the ground state. We initially analyze the free Klein–Gordon and Dirac fields, and then formulate non-abelian gauge theories in Γ d D . Using the S-matrix, the decay of particles is calculated in order to show the effect of the compactification. |
Keywords: | Quantum fields Toroidal topology c∗- and Lie algebra Compactification |
URI: | http://www.repositorio.ufba.br/ri/handle/ri/5445 |
Issue Date: | 2011 |
Appears in Collections: | Artigo Publicado em Periódico (FIS) |
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