Asymptotically free phi/sup 4/ theory. [Renormalization group, zero-momentum theorems, perturbation series]
Exact properties of asymptotically free gphi/sup 4/ theory with negative (renormalized) g are deduced by renormalization-group and other methods. It has been argued that the effective potential V (chi) for the model approaches - infinity for chi ..-->.. infinity, so that the model is inconsistent with positivity. It is shown here how this difficulty may be avoided because of deduced results which imply that actually V (chi) = const x chi/sup 2/. These results are exact zero-momentum theorems which state that the proper vertex functions (except for the inverse two-point function) vanish whenever one of their four-momentum arguments vanish. These theorems are deduced as a consequence of the fact that the exact field equation of the theory is invariant, apart from mass terms and mass counterterms, to the transformation phi (x) ..-->.. phi (x) + const, which only adds a constant (reflection-symmetry breaking) term to the field equation. This partial symmetry and the associated theorems arise as a consequence of renormalization: they are not true order by order in perturbation theory. The perturbation series in g for the vertex functions is therefore not an asymptotic expansion when a momentum vanishes. This is either a remarkable property of the model or an indication that the model really is unstable after all. (AIP)
- Research Organization:
- Center for Theoretical Physics, Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742
- OSTI ID:
- 7240107
- Journal Information:
- Phys. Rev., D; (United States), Vol. 14:12
- Country of Publication:
- United States
- Language:
- English
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