One-loop effective action for super-QCD

The path integral method with respect to the scalar (quark) superfields is used to obtain the effective action for fields with the quantum numbers of the mesons and their superpartners inN-1 super-QCD. The background fields include gauge superfields of the groupSU _L (N)xSU _R (N)xU _L(1)xU _R(1) and also Higgs superfields in the adjoint representation of the groupSU _L (N)xSU _R (N).St. Petersburg Wood Technology Academy. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 2, pp. 237–246, February, 1995.     

One-loop effective action for the gauge field in curved space-time

We consider the one-loop contribution of gluon fluctuations to the gauge-field effective action in a constant homogenous Abelian-like external (background) field in a space with nonzero curvature. We calculate the real and imaginary parts of the effective action and show that the chromomagnetic vacuum remains unstable in spite of the finite curvature of the space. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 1, pp. 123–129, October, 1998.     

One-loop effective action in the $$ \mathcal{N} $$=2 supersymmetric massive Yang-Mills field theory

We consider the =2 supersymmetric massive Yang-Mills field theory formulated in the =2 harmonic superspace. We present various gauge-invariant forms of writing the mass term in the action (in particular, using the Stueckelberg superfield), which result in dual formulations of the theory. We develop a gaugeinvariant and explicitly supersymmetric scheme of the loop expansion of the superfield effective action beyond the mass shell. In the framework of this scheme, we calculate gauge-invariant and explicitly =2 supersymmetric one-loop counterterms including new counterterms depending on the Stueckelberg superfield. We analyze the component structure of one of these counterterms. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 22–40, October, 2008.     

One-loop divergences in theories with an arbitrary nonminimal operator in curved space

We construct an explicit formula for the divergent part of the one-loop effective action for an arbitrary nonminimal operator in curved four-dimensional space. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 3, pp. 351–371, March, 1997.     

Holographic relation between p-adic effective action and string field theory

We consider two holographically related theories. As the first (d + 1)-dimensional theory, we consider a model in which the (d + 1)-dimensional space is the direct product of ? ^d and the half-axis ?₊ and in which the kinetic operator has a nonlocal term induced by the nonlocal kinetic operator of the p-adic effective action. It turns out that the kinetic operator in the second, holographically related, d-dimensional theory is the kinetic operator of the string field theory effective action.     

Lattice point theory of irractional ellipsoids with an arbitrary center

We shall consider positive definite quadratic formsQ inr2 variables of the almost diagonal shape where 2, and for 1j,Q _j is a positive definite quadratic form with integral coefficients inr _j variables, _j is a positive real number,r _j1 andr ₁+...+r =r Letb ₁,...,b _r be a system of real numbers with 0b _j<1. For x>0 letA(x) be the number of lattice points in the ellipsoidQ(u+b)x, letV(x) be the volume of this ellipsoid and letP(x)=A(x)-V(x). Our purpose is to find the exact order ofP(x); i. e., the numberf for which for each >0P(x)=O(x^f+) andP(x)=(x ^f–).     

Scattering theory for elliptic operators of arbitrary order

We prove the main theorems of scattering theory for selfadjoint elliptic partial differential operators of arbitrary order. Under various hypotheses we show that the wave operators exist and are complete, that the intertwining relations hold, and that the invariance principle holds. One of our main hypotheses is that each lower order coefficientq(x) satisfies. $$(1 + \left| x \right|)^\alpha \int\limits_{\left| {x - y} \right|< a} {\left| {q(y)} \right|dy \in L^p (E^n )}$$ for some α≥0,a>0 and forp≤∞ such that $$\alpha > 1 - \frac{{2n}}{{(n + 1)p}}$$      

One-loop counterterms in the Yang-Mills theory with a gauge-invariant ghost field Lagrangian

We calculate the one-loop renormalization constants Z ₁ and Z ₂ in the model with a gauge-invariant ghost field Lagrangian. We show that the model is asymptotically free and that the renormalization constants satisfy the same equation as in the ordinary Yang-Mills theory.     

Scalar field in an arbitrary dimension from the standpoint of higher-spin Gauge theory

We formulate the equations of motion of a free scalar field in the flat and AdS spaces of arbitrary dimension in the form of “higher-spin” covariant constancy conditions. The Klein-Gordon equation describes a nontrivial cohomology of a certain “σ_-complex.” The action principle for a scalar field is formulated in terms of the “higher-spin” covariant derivatives for an arbitrary mass in AdS_d and for a nonzero mass in the flat space. The free-field part of the constructed action coincides with the standard first-order Klein-Gordon action, but the interaction part is different because of the presence of an infinite set of auxiliary fields, which do not contribute at the free level. We consider the example of Yang-Mills current interaction and show how the proposed action generates the pseudolocally exact form of the matter currents in AdS_d. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 323–344, May, 2000.     

A general Galois theory for operations and relations in arbitrary categories

In this paper, we generalize the notions of polymorphisms and invariant relations to arbitrary categories. This leads us to a Galois connection that coincides with the classical case from universal algebra if the underlying category is the category of sets, but remains applicable no matter how the category is changed. In analogy to the situation in the classical case, we characterize the Galois closed classes by local closures of clones of operations and local closures of what we will introduce as clones of (generalized) relations. Since the approach is built on purely category-theoretic properties, we will also discuss the dualization of our notions.     

Bounds for mixtures of an arbitrary number of materials

This paper studies the problem of bounding the effective conductivity coefficients of mixtures made of several materials, in given proportions. Lower and upper bounds are obtained, and the optimality of these bounds is proven under certain hypotheses. Also, necessary and sufficient conditions for a mixture to attain the bounds are described. Some of the results were already known, but we give simpler proofs. Copyright © 2001 John Wiley & Sons, Ltd.     

Convergence theorems for continuous functions on an arbitrary interval

In this paper, we introduce a new iterative scheme for finding a fixed points of continuous functions on an arbitrary interval. The convergence theorems are also established. Further, the numerical examples comparing with Mann, Ishikawa and Noor iterations are demonstrated. Main results generalize and unify the corresponding ones announced in the literature.