Inconsistency of the λΦ^4 Field Theory in High-Dimensions Constructed from the Broken-Symmetry Phase : Particles and Fields

概要

論文の詳細を見る
We discuss the construction of the broken-symmetry λφ^4 theory from the lattice-regularized model defined on εZ^d (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 Γ_c as ε↓0 such that lim _<ε→0><φ_<ren>(x)>^<(ε)>≠0. In the case of 0<lim _<ε→0><φ_<ren>(x)>^<(ε)><∞, it is shown that the 3- and 4-point renormalized coupling constants vanish in the continuum limit ε↓0, as long as 0<λ(ε)<λ_0 for sufficiently small λ_0, in dimensions d>d_c (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 <φ_<ren>(x)>^<(ε)>→∞ as ε→0, the same type of triviality is derived for d>4. These results suggest that the consistency requirement of the λφ^4 theory obtained in this scheme leads to the result: <φ_<ren>(x)>^<(ε)>→0 as ε→0, i.e., no breakdown of the symmetry φ→-φ in all d>4 dimensions.
理論物理学刊行会の論文
1988-05-25