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arXiv · 1812.07087

Dimensional reduction of a finite-size scalar field model at finite temperature

E. Cavalcanti·J. A. Lourenço·C. A. Linhares·A. P. C. Malbouisson
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Abstract

We investigate the process of dimensional reduction of one spatial dimension in a thermal scalar field model defined in $D$ dimensions (inverse temperature and $D-1$ spatial dimensions). We obtain that a thermal model in $D$ dimensions with one of the spatial dimensions having a finite size $L$ is related to the finite temperature model with just $D-1$ spatial dimensions and no finite size. Our results are obtained for one-loop calculations and for any dimension $D$. For example, in $D=4$ we have a relationship between a thin film with thickness $L$ at finite temperature and a surface at finite temperature. We show that, although a strict dimensional reduction is not allowed, it is possible to define a valid prescription for this procedure.

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E. Cavalcanti, J. A. Lourenço, C. A. Linhares, A. P. C. Malbouisson. 2018-12-17. Dimensional reduction of a finite-size scalar field model at finite temperature. https://doi.org/10.1103/physrevd.99.025007

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