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Prog. Theor. Phys. Vol. 79 No. 5 (1988) pp. 1217-1248

[ Full Text PDF : FREE ACCESS (1340K) ]

Inconsistency of the λΦ4 Field Theory in High-Dimensions Constructed from the Broken-Symmetry Phase

Kei-ichi Kondo

Department of Physics, Nagoya University, Nagoya 464

(Received December 24, 1987)

Abstract:

We discuss the construction of the broken-symmetry λφ4 theory from the lattice-regularized model defined on εZd (d-dimensional hypercubic lattice with lattice spacing ε) in the sense that the bare parameter (e.g., λ= λ(ε)) as a function of ε is adjusted approach the critical manifold Γc as ε↓0 such that limε→0 <φren(x) >(ε) ≠0. In the case of 0 < limε→0 <φren(x)>(ε) < ∞, it is shown that the 3- and 4-point renormalized coupling constant vanish in the continuum limit ε↓0, as long as 0 < λ(ε) < λ0 for sufficiently small λ0, in dimensions d > dc (upper critical dimension) where the critical exponent δ of the magnetization on the critical isotherm line takes its classical (mean-field) value δ= 3. Even for the renormalization which allows <φren(x) >(ε) →∞ as ε→0, the same type of triviality is derived for d > 4. These results suggest that the consistency requirement of the λφ4 theory obtained in this scheme leads to the result: <φren(x)>(ε) →0 as ε→0, i.e., no breakdown of the symmetry φ→-φ in all d > 4 dimensions.


URL : http://ptp.ipap.jp/link?PTP/79/1217/
DOI : 10.1143/PTP.79.1217

[ Full Text PDF : FREE ACCESS (1340K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 88 No. 4 (1992) pp. 737-749 :
    Strong Coupling Unquenched QED. II
    Kei-ichi Kondo and Hajime Nakatani

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