Gell-Mann-Low function in the ϕ4 theory

An algorithm is proposed for the determination of the asymptotics of a sum of a perturbation series from the given values of its coefficients in the strong-coupling limit. When applied to the ?⁴ theory, the algorithm yields the β(g)∝g ^α behavior with α≈1 at large g for the Gell-Mann-Low function.     

A new proof of the existence and nontriviality of the continuum ϕ 2 4 and ϕ 3 4 quantum field theories

We use Schwinger-Dyson equations combined with rigorous “perturbation-theoretic” correlation inequalities to give a new and extremely simple proof of the existence and nontriviality of the weakly-coupled continuum ? ₂ ⁴ and ? ₃ ⁴ quantum field theories, constructed as subsequence limits of lattice theories. We prove an asymptotic expansion to order λ or λ² for the correlation functions and for the mass gap. All Osterwalder-Schrader axioms are satisfied except perhaps Euclidean (rotation) invariance.     

Borel summability of the mass and theS-matrix in ϕ4 models

We show that in the ₂ ⁴ theory, the physical mass and the two-bodyS-matrix are Borel summable in the coupling constant at =0.     

Analyticity of scattering for the ϕ4 theory

We consider scattering for the equation (+m ²)+³=0 on four-dimensional Minkowski space. Form>0, one-to-one and onto wave operatorsW _± :HH are known to exist for all 0, whereH denotes the Hilbert space of finite-energy Cauchy data. We prove that the maps (,u)W _± (u) and (,u)(W _± )^–1 (u) are continuous from [0, )×H toH, and extend to real-analytic functions from an open neighborhood of {0}×H×{0}×H to the Hilbert spaceH _–1 of Cauchy data with Poincaré-invariant norm. Form=0, wave operatorsW _± are known to exist as diffeomorphisms ofH for all 0, where hereH denotes the Hilbert space of finite Einstein energy Cauchy data. In this case we prove that the maps (,u)(W _± ) (u) and (,u)(W _± )^–1 (u) extend to real-analytic functions from a neighborhood of [0, )×H×H toH.     

Background field method for nonlinear σ-model in stochastic quantization

We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model.     

Leading RG logs in ϕ4 theory

We find the leading RG logs in ϕ⁴ theory for any Feynman diagram with 4 external edges. We obtain the result in two ways. The first way is to calculate the relevant terms in Feynman integrals. The second way is to use the RG invariance based on the Lie algebra of graphs introduced by Connes and Kreimer.     

Periodicity in the Appearance of Intervals of the Reversal of the Magnetic Moment of a ϕ0 Josephson Junction

JETP Letters - The uniaxial anisotropy and kinetics of the transformation of the domain structure in a ferrimagnetic GdFeCo film exchange-coupled to the IrMn antiferromagnet have been studied in a...     

On the geometric origin of the equation ϕ,11 — ϕ,22 = eϕ — e-2ϕ

It is shown that the equation ,11 — ,22 = e — e^-2 determines the intrinsic geometry of the two-dimensional affine sphere in the three-dimensional unimodular affine space like the sine-Gordon equation describes the metric on the surface of a constant negative curvature in the three-dimensional Euclidean space. The linear equations that determine the moving frame on the affine sphere are the Lax operators to the equation ,11 — ,22 = e — e^-2.     

Representation of an interaction in the formalism of operator BRST quantization for the standard electroweak theory in the Rξ gauge

An operator BRST quantization of the spontaneously broken SU(2)×U(1) electroweak theory is carried out in the R gauge. A representation is found for the interaction.Leninist Communist Youth League, Tomsk Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 79–83, July, 1992.     

A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

The ϕ 2 4 quantum field as a limit of Sine-Gordon fields

We exhibit the λ? 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 ?. As a by-product, let (?,dμ) be a Gaussian random field, ? _K (1≦κ<∞) a regularization of ?, andV a function satisfying:

1. V(? _K )≧?ak ^α
2. ∥V(?) ?V(? _K )∥ _p≦bp ^β k ^?γ, 2≦p < ∞

Thene ^?V(?)∈L ¹(dμ) provided α(β?1)<γ.     

Center-of-mass quantization of excitons and Fabry–Perot modes of the polariton in ZnSe epilayers

Reflectance properties of ZnSe epilayers grown on GaAs substrates are studied at 80 K. Oscillation features are observed in the region of exciton resonance which are significantly different depending on the epilayer thickness L. For optically thin layers with thickness in the range of several tens of nanometer, reflectance oscillations appear above the light-hole (lh) exciton, while for optically thick layers with thickness in the range of a micrometer, reflectance oscillations appear between 1s and 2s excitons. These oscillations are interpreted as the quantized levels of the exciton center-of-mass motion in the lower branch of the polariton for optically thin layers and Fabry–Perot modes in the upper branch of the polariton for optically thick layers, respectively. The reflectance data are analyzed in the frame work of a dielectric function with a polariton dispersion.