ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We exhibit the λϕ 2 4 quantum field theory as the limit of Sine-Gordon fields as suggested by the identity $$\varphi ^4 /4! = \mathop {\lim }\limits_{\varepsilon \to 0} (\varepsilon ^{ - 4} \cos \varepsilon \varphi - \varepsilon ^{ - 4} + \tfrac{1}{2}\varepsilon ^{ - 2} \varphi ^2 ).$$ The proofs of finite volume stability for the two models, due to Nelson and Fröhlich respectively, are unrelated. We find a generalized stability argument that incorporates ideas from both of the simpler cases. The above limit, for the Schwinger functions, then proceeds uniformly in ɛ. As a by-product, let (ϕ,dμ) be a Gaussian random field, ϕ K (1≦κ〈∞) a regularization of ϕ, andV a function satisfying: (i) V(ϕ K )≧−ak α (ii) ∥V(ϕ) −V(ϕ K )∥ p≦bp β k −γ, 2≦p 〈 ∞ Thene −V(ϕ)∈L 1(dμ) provided α(β−1)〈γ.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01940770
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