The Non-Trivial Phase of $\PHI ^4$-Theory in a Renormalisation Group Invariant Approach

Details The Non-Trivial Phase of $\PHI ^4$-Theory in a Renormalisation Group Invariant Approach The Non-Trivial Phase of $\PHI ^4$-Theory in a Renormalisation Group Invariant Approach

1993-03-09

arxiv.org/abs/hep-ph/9303235v1

Phys.Lett. B308 (1993) 279-285

Physics

High Energy Physics

High Energy Physics - Phenomenology

11 LaTex pages (2 figures available on request), UNITUE-THEP-2-1993

Scientific paper

10.1016/0370-2693(93)91285-U

Massless $\phi^{4}$-theory is investigated in zero and four space-time dimensions. Path-integral linearisation of the $\phi ^{4}$-interaction defines an effective theory, which is investigated in a loop-expansion around the mean field. In zero dimensions this expansion converges rapidly to the exact potential obtained numerically. In four dimensions its lowest order (mean-field approximation) produces a real and convex effective potential. Two phases are found. In one the renormalisation group improved one-loop effective potential is recovered as the leading contribution near the classical minimum. This phase, however, is unstable. The second (precarious) phase is found to have lower vacuum energy density. In this phase a dynamical mass is generated. The results are renormalisation group invariant.

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