Summation of diagrams in N=1 supersymmetric electrodynamics regularized by higher derivatives

For the massless N=1 supersymmetric electrodynamics regularized by higher derivatives, we partially sum the Feynman diagrams that define the divergent part of the two-point Green’s function and cannot be found from Schwinger—Dyson equations and Ward identities. The result can be written as a special identity for Green’s functions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 385–401, March, 2006.     

Higher covariant derivatives

We obtain a composition formula for the higher covariant derivatives on a vector bundle over a manifold. The formula generalizes the classical Leibniz product rule for the derivative. We also obtain, as a corollary, a generalization of the author’s theorem about the double exponential map to the case of multiple maps.     

Contribution of matter fields to the Gell-Mann-Low function for the $$\mathcal{N} = 1$$ supersymmetric Yang-Mills theory regularized by higher covariant derivatives

We use the Schwinger-Dyson equations and Slavnov-Tailor identities to obtain the contribution of matter fields to the Gell-Mann-Low function for the supersymmetric Yang-Mills theory regularized by higher covariant derivatives. We discuss the possible deviation of the result from the corresponding contribution to the exact Novikov-Shifman-Vainshtein-Zakharov β-function. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 3, pp. 441–460, March, 2007.     

Two-loop Gell-Mann-Low function of the <Emphasis Type="Italic">N</Emphasis>=1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives

We calculate the two-loop Gell-Mann-Low function for the N=1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives. We show that the integrals determining this function reduce to total derivatives and can be easily calculated analytically. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 398–414, June, 2008.     

Curvature tensors and covariant derivatives

Summary The problems considered here are of two types.(i) What are implications of vanishing k-th covariant derivatives of curvature tensors?(ii) Under what conditions on curvature tensors, does the k-th covariant derivative ∇^kT=0 for a tensor T mean ∇T=0? Entrato in Redazione il 16 Maggio 1972.     

Higher covariant derivative regularization for calculations in supersymmetric theories

A variant of the higher covariant derivative regularization is used for calculation of a two-loop β-function for the general renormalizable N = 1 supersymmetric theory. It is shown that the β-function is given by integrals of total derivatives. Partially this can be explained by substituting solutions of Slavnov-Taylor identities into the Schwinger-Dyson equations.     

General covariant derivatives for general connections

In this paper we introduce the general covariant derivatives of vertical-valued tensor fields with respect to a general connection on a fibered manifold and a classical connection on the base. We prove that the general covariant derivatives satisfy the general Ricci and the general Bianchi identities.     

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.     

A simplified version of higher covariant derivative regularization

A simplified version of the higher covariant derivative (HCD) regularization for the Yang-Mills theory is constructed. This makes the HCD method suitable for actual calculations. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 122, No. 3, pp. 426–434, March, 2000.     

On quantization of general covariant theories. The dynamic quantization

A new method for quantizing general covariant theories, which includes regularization and a calculation scheme, is proposed. The method is based on the Dirac theory of quantizing constrained systems. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 1, pp. 132–141.     

Asymptotic behavior of the regularized minimizer of an energy functional in higher dimensions

This paper is concerned with the asymptotic behavior of the regularized minimizer uε=(uε1,uε2,…,uεn+1) of an energy functional

     

Two natural metrics and their covariant derivatives on a manifold of embeddings

OnE(M, ⁿ ), the Fréchet-manifold of all smooth embeddings of a smooth, compact, closed, orientable manifoldM (of dimensionn-1) into ⁿ two natural metricsG and are considered. The metric plays a central rôle in elasticity theory. Using a generalised notion of the Fréchet derivative their respective spraysS and and the correspoonding Levi-Civita connections are computed. BothS and are smooth in a well defined sense. In contrast toS the spray turns out to be trivial.     

Generalized uniformly continuous semigroups and semilinear hyperbolic systems with regularized derivatives

We adopt the theory of uniformly continuous operator semigroups for use in Colombeau generalized function spaces. The main objective is to find a unique solution to a class of semilinear hyperbolic systems with singularities. The idea of regularized derivatives is to transform unbounded differential operators into bounded, integral ones. This idea is used here to permit working with uniformly continuous operators.     

Generalized uniformly continuous semigroups and semilinear hyperbolic systems with regularized derivatives

We adopt the theory of uniformly continuous operator semigroups for use in Colombeau generalized function spaces. The main objective is to find a unique solution to a class of semilinear hyperbolic systems with singularities. The idea of regularized derivatives is to transform unbounded differential operators into bounded, integral ones. This idea is used here to permit working with uniformly continuous operators.