Asymptotic freedom in a scalar field theory on the lattice

Abstract

An alternative model to the trivial ${\varphi }^4$-theory of the standard model of weak interactions is suggested, which embodies the Higgs-mechanism, but is free of the conceptual problems of standard ${\varphi }^4$-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.

10 pages, LaTeX, one figure and a motivation for the particular type of action added

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Cited by in corpus (4)

• General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
• Kurt Symanzik - a stable fixed point beyond triviality
• Flow equation for Halpern-Huang directions of scalar O(N) models
• On the Landau Ginzburg theory of MAG projected SU(2) lattice gauge theory