The long-range interaction in massless (lambda Phi^4)_4 theory

Details The long-range interaction in massless (lambda Phi^4)_4 theory The long-range interaction in massless (lambda Phi^4)_4 theory

2008-06-23

arxiv.org/abs/0806.3690v2

Mod.Phys.Lett.A24:261-271,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, LaTeX, 5 figures (.eps)

Scientific paper

10.1142/S0217732309028990

Does massless (lambda Phi^4)_4 theory exhibit spontaneous symmetry breaking (SSB)? The raw 1-loop result implies that it does, but the "RG-improved" result implies the opposite. I argue that the appropriate "low-energy effective theory" is a nonlocal field theory involving an attractive, long-range interaction Phi^2(x) Phi^2(y)/z^4, where z=|x-y|. RG improvement then requires running couplings for both this interaction and the original pointlike interaction. A crude calculation in this framework yields SSB even after "RG improvement" and closely agrees with the raw 1-loop result.

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