Asymptotic freedom in a scalar field theory on the lattice

Details Asymptotic freedom in a scalar field theory on the lattice Asymptotic freedom in a scalar field theory on the lattice

1997-02-06

arxiv.org/abs/hep-ph/9702271v2

Mod.Phys.Lett. A13 (1998) 2495-2502

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1142/S0217732398002655

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