Abstract:
|
The O(N)-symmetric generalization of λ
φ
4
theory is studied in the Gaussian-effective-potential (GEP) approach. It is shown that the GEP encompasses and transcends the leading-order 1/N expansion results. We find two distinct, nontrivial versions of the (3+1)-dimensional theory: (i) ‘‘precarious
φ
4
theory,’’ with negative, infinitesimal
λ
B
, which coincides with the 1/N result; and (ii) ‘‘autonomous
φ
4
theory,’’ with positive, infinitesimal
λ
B
and an infinite wave-function renormalization, which is inaccessible to perturbative or 1/N methods, and could well have eluded lattice-based approaches. ‘‘Autonomous
φ
4
theory’’ can exhibit spontaneous symmetry breaking, and we speculate on its relevance for the Higgs mechanism. |