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arXiv · hep-ph/9702271

Asymptotic freedom in a scalar field theory on the lattice

K. Langfeld·H. Reinhardt
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Abstract

An alternative model to the trivial $ϕ^4$-theory of the standard model of weak interactions is suggested, which embodies the Higgs-mechanism, but is free of the conceptual problems of standard $ϕ^4$-theory. We propose a N-component, O(N)-symmetric scalar field theory, which is originally defined on the lattice. The model can be motivated from SU(2) gauge theory. Thereby the scalar field arises as a gauge invariant degree of freedom. The scalar lattice model is analytically solved in the large N limit. The continuum limit is approached via an asymptotically free scaling. The renormalized theory evades triviality, and furthermore gives rise to a dynamically formed mass of the scalar particle.

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K. Langfeld, H. Reinhardt. 1997-06-26. Asymptotic freedom in a scalar field theory on the lattice. https://doi.org/10.1142/s0217732398002655

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