The Experts below are selected from a list of 10074 Experts worldwide ranked by ideXlab platform
Konstantin Viktorovich Stepanyantz - One of the best experts on this subject based on the ideXlab platform.
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The higher Covariant Derivative regularization as a tool for revealing the structure of quantum corrections in supersymmetric gauge theories.
arXiv: High Energy Physics - Theory, 2019Co-Authors: Konstantin Viktorovich StepanyantzAbstract:We discuss why the Slavnov higher Covariant Derivative regularization appeared to be an excellent instrument for investigating quantum corrections in supersymmetric gauge theories. For example, it allowed to demonstrate that the $\beta$-function in these theories is given by integrals of double total Derivatives and to construct the NSVZ renormalization prescription in all loops. It was also used for deriving the non-renormalization theorem for the triple gauge-ghost vertices. With the help of this theorem the exact NSVZ $\beta$-function was rewritten in a new form, which revealed its perturbative origin. Moreover, in the case of using the higher Covariant Derivative regularization it is possible to construct a method for obtaining the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories, which simplifies the calculations in a great extent. This method is illustrated by an explicit two-loop calculation made in the general $\xi$-gauge.
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Multiloop calculations in supersymmetric theories with the higher Covariant Derivative regularization
Journal of Physics: Conference Series, 2012Co-Authors: Konstantin Viktorovich StepanyantzAbstract:Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not self-consistent. A consistent regularization, which does not break the supersymmetry, is the higher Covariant Derivative regularization. However, the integrals obtained with this regularization can not be usually calculated analytically. We discuss application of this regularization to the calculations in supersymmetric theories. In particular, it is demonstrated that integrals defining the beta-function are possibly integrals of total Derivatives. This feature allows to explain the origin of the exact NSVZ beta-function, relating the beta-function with the anomalous dimensions of the matter superfields. However, integrals for the anomalous dimension should be calculated numerically.
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multiloop calculations in supersymmetric theories with the higher Covariant Derivative regularization
arXiv: High Energy Physics - Theory, 2012Co-Authors: Konstantin Viktorovich StepanyantzAbstract:Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not self-consistent. A consistent regularization, which does not break the supersymmetry, is the higher Covariant Derivative regularization. However, the integrals obtained with this regularization can not be usually calculated analytically. We discuss application of this regularization to the calculations in supersymmetric theories. In particular, it is demonstrated that integrals defining the β-function are possibly integrals of total Derivatives. This feature allows to explain the origin of the exact NSVZ β-function, relating the β-function with the anomalous dimensions of the matter superfields. However, integrals for the anomalous dimension should be calculated numerically.
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Quantum corrections in N = 1 supersymmetric theories with cubic superpotential, regularized by higher Covariant Derivatives
Physics of Particles and Nuclei Letters, 2011Co-Authors: Konstantin Viktorovich StepanyantzAbstract:Using the higher Covariant Derivative regularization we calculate a two-loop β-function for the N = 1 supersymmetric Yang-Mills theory with the matter superfields, containing the cubic superpotential. It is found that all integrals, defining this function, are integrals of total Derivatives.
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Higher Covariant Derivative regularization for calculations in supersymmetric theories
Proceedings of the Steklov Institute of Mathematics, 2011Co-Authors: Konstantin Viktorovich StepanyantzAbstract: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.
H. Morales - One of the best experts on this subject based on the ideXlab platform.
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The Standard Model and the Generalized Covariant Derivative
arXiv: High Energy Physics - Phenomenology, 1999Co-Authors: M. Chaves, H. MoralesAbstract:The generalized Covariant Derivative, that uses both scalar and vector bosons, is defined. It is shown how a grand unified theory of the Standard Model can be constructed using a generalized Yang-Mills theory.
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UNIFICATION OF SU(2)⊗U(1) USING A GENERALIZED Covariant Derivative AND U(3)
Modern Physics Letters A, 1998Co-Authors: M. Chaves, H. MoralesAbstract:A generalization of the Yang–Mills Covariant Derivative, that uses both vector and scalar fields and transforms as a four-vector contracted with Dirac matrices, is used to simplify the Glashow–Weinberg–Salam model. Since SU(3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U(3) to obtain all the correct quantum numbers. A surplus gauge scalar boson emerges in the process, but it uncouples from all other particles.
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unification of su 2 u 1 using a generalized Covariant Derivative and u 3
Modern Physics Letters A, 1998Co-Authors: M. Chaves, H. MoralesAbstract:A generalization of the Yang–Mills Covariant Derivative, that uses both vector and scalar fields and transforms as a four-vector contracted with Dirac matrices, is used to simplify the Glashow–Weinberg–Salam model. Since SU(3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U(3) to obtain all the correct quantum numbers. A surplus gauge scalar boson emerges in the process, but it uncouples from all other particles.
Koh-ichi Nittoh - One of the best experts on this subject based on the ideXlab platform.
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Integer- and Non-Integer-Shift of the Chern-Simons Coupling under a Local Higher Covariant Derivative Regulator
arXiv: High Energy Physics - Theory, 2002Co-Authors: Koh-ichi NittohAbstract:The Chern-Simons coupling shift is calculated within the framework of the hybrid regularization based on a local higher Covariant Derivative regulator. When the Yang-Mills term is present in the theory the well-know integer-shift is obtained, but is absent, the shift value is non-integer. These results show a possibility that a non-integer-shift can be derived using a local higher Covariant Derivative and also suggest that the Yang-Mills term plays an important role in the integer-shift of the Chern-Simons coupling.
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CONSISTENCY OF THE HYBRID REGULARIZATION WITH HIGHER Covariant Derivative AND INFINITELY MANY PAULI–VILLARS
International Journal of Modern Physics A, 2001Co-Authors: Koh-ichi NittohAbstract:We study the regularization and renormalization of the Yang–Mills theory in the framework of the manifestly invariant formalism, which consists of a higher Covariant Derivative with an infinitely many Pauli–Villars fields. Unphysical logarithmic divergence, which is the problematic point on the Slavnov method, does not appear in our scheme, and the well-known value of the renormalization group functions are derived. The cancellation mechanism of the quadratic divergence is also demonstrated by calculating the vacuum polarization tensor of the order of Λ0 and Λ-4. These results are the evidence that our method is valid for intrinsically divergent theories and is expected to be available for the theory which contains the quantity depending on the space–time dimensions, like supersymmetric gauge theories.
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consistency of the hybrid regularization with higher Covariant Derivative and infinitely many pauli villars
arXiv: High Energy Physics - Theory, 2000Co-Authors: Koh-ichi NittohAbstract:We study the regularization and renormalization of the Yang-Mills theory in the framework of the manifestly invariant formalism, which consists of a higher Covariant Derivative with an infinitely many Pauli-Villars fields. Unphysical logarithmic divergence, which is the problematic point on the Slavnov's method, does not appear in our scheme, and the well-known vale of the renormalization group functions are derived. The cancellation mechanism of the quadratic divergence is also demonstrated by calculating the vacuum polarization tensor of the order of $\Lambda^0$ and $\Lambda^{-4}$. These results are the evidence that our method is valid for intrinsically divergent theories and is expected to be available for the theory which contains the quantity depending on the space-time dimensions, like supersymmetric gauge theories.
Christian Corda - One of the best experts on this subject based on the ideXlab platform.
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The commutator algebra of Covariant Derivative as general framework for extended gravity. The Rastall theory case and the role of the torsion
International Journal of Geometric Methods in Modern Physics, 2017Co-Authors: Ignazio Licata, Hooman Moradpour, Christian CordaAbstract:In this short review, we discuss the approach of the commutator algebra of Covariant Derivative to analyze the gravitational theories, starting from the standard Einstein’s general theory of relativity (GTR) and focusing on the Rastall theory. After that, we discuss the important role of the torsion in this mathematical framework. In the appendix of the paper, we analyze the importance of the nascent gravitational wave (GW) astronomy as a tool to discriminate among the GTR and alternative theories of gravity.
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the commutator algebra of Covariant Derivative as general framework for extended gravity the rastall theory case and the role of the torsion
arXiv: General Relativity and Quantum Cosmology, 2017Co-Authors: Ignazio Licata, Hooman Moradpour, Christian CordaAbstract:In this short review, we discuss the approach of the commutator algebra of Covariant Derivative to analyse the gravitational theories, starting from the standard Einstein's general theory of relativity and focusing on the Rastall theory. After that, we discuss the important role of the torsion in this mathematical framework. In the Appendix of the paper we analyse the importance of the nascent gravitational wave astronomy as a tool to discriminate among the general theory of relativity and alternative theories of gravity.
Peter B. Gilkey - One of the best experts on this subject based on the ideXlab platform.
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Geometric realizability of Covariant Derivative Kähler tensors for almost pseudo-Hermitian and almost para-Hermitian manifolds
Annali di Matematica Pura ed Applicata, 2011Co-Authors: Miguel Brozos-vázquez, Eduardo García-río, Peter B. Gilkey, Luis HervellaAbstract:The Covariant Derivative of the Kahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can be realized geometrically.
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Geometric Realizability of Covariant Derivative K
arXiv: Differential Geometry, 2010Co-Authors: Miguel Brozos-vázquez, Eduardo García-río, Peter B. Gilkey, Luis HervellaAbstract:The Covariant Derivative of the K\"ahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can be realized geometrically.
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Geometric Realizability of Covariant Derivative K\"ahler Tensors for almost Pseudo-Hermitian and almost Para-Hermitian Manifolds
arXiv: Differential Geometry, 2010Co-Authors: Miguel Brozos-vázquez, Eduardo García-río, Peter B. Gilkey, Luis HervellaAbstract:The Covariant Derivative of the K\"ahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can be realized geometrically.
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THE STRUCTURE OF ALGEBRAIC Covariant Derivative CURVATURE TENSORS
International Journal of Geometric Methods in Modern Physics, 2004Co-Authors: José Carlos Díaz-ramos, Eduardo García-río, Bernd Fiedler, Peter B. GilkeyAbstract:We use the Nash embedding theorem to construct generators for the space of algebraic Covariant Derivative curvature tensors.
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Jordan Szabo algebraic Covariant Derivative curvature tensors
arXiv: Differential Geometry, 2002Co-Authors: Peter B. Gilkey, Raina Ivanova, Iva StavrovAbstract:We show that if $\nabla R$ is a Jordan Szabo algebraic Covariant Derivative curvature tensor on a vector space of signature (p,q), where q is odd and p is less than q or if q is congruent to 2 mod 4 and if p is less than q-1, then $\nabla R=0$. This algebraic result yields an elementary proof of the geometrical fact that any pointwise totally isotropic pseudo-Riemannian manifold with such a signature (p,q) is locally symmetric.
