Antisymmetric tensor fields and the Weyl gauge theory

The aim of the present paper is to find a spinor current—a source—in the Weyl non-Abelian gauge theory whose distinguishing feature is that it involves no abstract gauge space. It is shown that the desired spinor representation of the Weyl gauge group can be constructed in the space of antisymmetric tensor fields in the form of a 16-component quantity for which a gauge-invariant Lagrangian is established. The relationship between the Weyl non-Abelian gauge potential and the Cartan torsion field, and the question of where the interactions in question could manifest are discussed. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 112–123, October, 1997.     

Non-Abelian tensor square and related constructions of p-groups

Archiv der Mathematik - Let G be a group. We denote by $$nu (G)$$ a certain extension of the non-Abelian tensor square $$[G,G^{varphi }]$$ by $$G times G$$. We prove that if G is a finite potent...     

Non-Abelian gauge theories,prepotentials, and Abelian differentials

We discuss particular solutions of integrable systems (starting from the well-known dispersionless KdV and Toda hierarchies) that most directly define the generating functions for the Gromov-Witten classes in terms of a rational complex curve. From the mirror theory standpoint, these generating functions can be identified with the simplest prepotentials of complex manifolds, and we present some new exactly calculable examples of such prepotentials. For higher-genus curves, which in this context correspond to non-Abelian gauge theories via the topological string/gauge duality, we construct similar solutions using an extended basis of Abelian differentials, generally with extra singularities at the branch points of the curve. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 2, pp. 220–242, May, 2009.     

Natural operators on tensor fields

Natural operators on tensor fields of different types are classified. We abstain from any assumptions such as symmetry or additional structures and consider arbitrary tensor fields.     

Symmetric tensor fields of bounded deformation

We introduce and study spaces of symmetric tensor fields of bounded deformation for tensors of arbitrary order, i.e., where the symmetrized derivative is still a Radon measure. A Sobolev–Korn type estimate, a boundary trace theorem and continuous as well as compact embedding properties into Lebesgue spaces are obtained, showing that these spaces can be regarded as a natural generalization of the spaces of bounded deformation to higher-order symmetric tensors.     

Symmetric energy-momentum tensor of spinor fields

We construct a symmetric energy-momentum tensor for spinor fields with an arbitrary Lagrange function on Riemannian space-time manifolds. We show that this tensor can be considered as the metric energy-momentum tensor.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 2, pp. 306–314, August, 1996.     

On operators associated with tensor fields

The aim of this paper is to introduce some operators which are applied to pure tensor fields. In this context Tachibana, Vishnevskii, Yano–Ako operators and their generalizations can be found.     

Mixed-symmetry massless gauge fields in AdS5

Using the su(2, 2) spinor language, we describe free mixed-symmetry massless bosonic and fermionic gauge fields of arbitrary spins in the AdS₅ space. We construct manifestly covariant action functionals and derive field equations. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 1, pp. 47–59, October, 2006.     

Theory of invariants of structural tensor fields

Systems of algebraic, differential, and conformal concomitants of structures on manifolds and in general vector bundles, defined by fields of covariant (contravariant) tensors of arbitrary valence, are constructed. As a preliminary, there is given a systematic survey of the theory of fiberwise and connecting tensor fields of vector bundles of Banach type and their covariant differentiation.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 17, pp. 51–86, 1985.     

A Korn's inequality for incompatible tensor fields

We prove a Korn-type inequality for bounded Lipschitz domains in and non-symmetric square integrable tensor fields having square integrable rotation . For skew-symmetric P or compatible our estimate reduces to non-standard variants of Poincaré's or Korn's first inequality, respectively, for which our new estimate can be viewed as a common generalized version. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)