$φ^4$ Field theory on a Lie group

Details $φ^4$ Field theory on a Lie group $φ^4$ Field theory on a Lie group

2000-07-22

arxiv.org/abs/hep-th/0007180v2

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, AMS-LaTeX

Scientific paper

The $\phi^4$ field model is generalized to the case when the field $\phi(x)$ is defined on a Lie group: $S[\phi]=\int_{x\in G} L[\phi(x)] d\mu(x)$, $d\mu(x)$ is the left-invariant measure on a locally compact group $G$. For the particular case of the affine group $G:x'=ax+b,a\in\R_+, x,b \in \R^n$ t he Feynman perturbation expansion for the Green functions is shown to have no ultra-violet divergences for certain choice of $\lambda(a) \sim a^\nu$.

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