Skew-symmetric Tensor Research Articles

On transversely isotropic, orthotropic and relative isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Part II: The representations for three dimensional transversely isotropic functions

There are five kinds of transversely isotropic groups which define the symmetry properties of three dimensional materials which are referred to as being transversely isotropic. In this part, we derive the complete representations for three dimensional transversely isotropic scalar-valued, vector-valued, symmetric tensor-valued and skew-symmetric tensor-valued functions of symmetric tensors, skew-symmetric tensors and vectors. The irreducibility of the representations is proved in Part III.

On transversely isotropic, orthotropic and relative isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Part V: The irreducibility of the representations for three dimensional orthotropic functions and the summary

In this part, the irreducibility of the representations derived in Part IV for three dimensional orthotropic scalar-valued, vector-valued, symmetric tensor-valued and skew-symmetric tensor-valued functions of symmetric tensors, skew-symmetric tensors and vectors is proved. Finally, a summary for all of this five-part paper is also given.

On the representations for isotropic vector-valued, symmetric tensor-valued and skew-symmetric tensor-valued functions

In this paper, we give a new derivation procedure for determining the representations for 3- and 2-dimensional isotropic vector-valued, symmetric tensor-valued and skew-symmetric tensorvalued functions of vectors, symmetric tensors and skew-symmetric tensors. Simplified representations for isotropic scalar-valued and vector-valued functions are suggested.

Tensors and manifolds: with applications to mechanics and relativity

Vector spaces Multilinear mappings and dual spaces Tensor product spaces Tensors Symmetric and skew-symmetric tensors Exterior (Grassman) algebra The tangent map of real cartesian spaces Topological spaces Differentiable manifolds Submanifolds Vector fields, 1-forms, and other tensor fields Exterior differentiation and integration of differential forms The flow, and the lie derivative of a vector field Integrability conditions for distributions of a vector field Integrability conditions for distributions and for Pfaffian systems Pseudo-riemannian geometry Connection 1-forms Connections on manifolds Mechanics Additional topics in mechanics A spacetime Some physics on Minkowski spacetime Einstein spacetimes Spacetimes near an isolated star Nonempty spacetimes.

New Lie-algebraic structures in nonlinear problems of quantum optics and laser physics

New Lie-algebraic structures (polynomial deformations of Lie algebras) are revealed in some problems of quantum optics and laser physics. Specifically, deformations of oscillator algebras due to extensions of unitary algebras by their symmetric and skew-symmetric tensors are shown to be algebras of dynamic symmetry (ADS) in models of n-photon processes with internal symmetries. Similarly, deformed algebras sud(2) are found as ADS in the context of generalized Dicke models and frequency conversion models. We also briefly discuss some possible schemes of employing the results to solving physical problems.

Sulla relazione fra il principio di Hamilton ed il principio dell'azione stazionaria nella dinamica relativistica di un corpuscolo

We show that within the relativistic dynamics of a particle the Hamilton's action yields the mechanical contribution of the action which is assumed in the space-time manifold by means of the least action principle. Furthermore, after introducing the four-potential and the skew-symmetric double tensor describing the field, we determine a new four-dimensional differential equation of motion for a particle, where there are involved the aforementioned four-dimensional quantities.

Theory of symmetry classes.

Although a great deal of work has gone into construction of the irreducible representations of the symmetric group n (and of the general linear group) a simple, intuitive characterization of the symmetry classes is missing. Relying on a systematic distinction between permutations of variables and permutations of places, we provide two such characterizations, showing that elements belonging to any such symmetry class can be described in one of two ways: (i) as the solutions of explicitly given (though not independent) sets of linear equations or (ii) as linear combinations of "simple" elements of a given symmetry class, a simple element being a generalization to an arbitrary symmetry class of the notion of a decomposable skew-symmetric tensor.

A quaternion representation of the Lorentz group for classical physical applications

A special quaternion representation is constructed for a pair of relativistic vectors and skew-symmetric tensors on the basis of the group theory of Lorentz transformations. The construction has considerable advantages over the conventional vector-tensor description. It is pointed out that pairs of Minkowski vectors as well as certain scalars and skew-symmetric tensors can also be interpreted as simple components of more complex physical quantities, each of them expressed by a single quaternion. As an example a concise relativistic quaternion formulation of Maxwell's electrodynamics is presented. The relativistic covariance can be maintained even for the existence of magnetic monopoles.

Covariantly constant tensors and holonomy structure in general relativity

This paper attempts to give a comprehensive discussion of space-times that admit vector fields or second-order symmetric or skew-symmetric tensor fields which are covariantly constant or recurrent. The relationship between such space-times M and their holonomy group is given.

On the representation of two-dimensional isotropic functions

The complete irreducible representation of scalar-valued, vector-valued, symmetric tensor-valued and skew-symmetric tensor-valued isotropic functions of an arbitrary number of two-dimensional symmetric tensors, vectors and skew-symmetric tensors are derived. The irreducibility of the different representations are proven.

Multichanel extensometric measurement of dynamic processes using a calibration pulse

. I. K. Senchenkov, V. G. Karnaukhov, and V. I. Kozlov, "On the theory of the governing equations of nonlinear thermoviscoelasticity for periodic strain," Prikl. Mekh., 22, No. 8, 97-104 (1986). I. K. Senchenkov, V. G. Karnaukhov, V. I. Kozlov, and O. P. Chervinko, "On the question of simple strain in problems on vibrations and heating of nonlinear viscoelastic bodies," Prikl. Mekh., 22, No. 9, 82-90 (1986). I. K. Senchenkov, "Approximate formulation of the coupled problems of nonlinear thermoviscoelasticity for harmonic actions," Prikl. Mekh., 21, No. 2, 91-99 (1985). J. P. Boehler and J. Raclin, "Representation irreductibles des functions tensorielles non-polynomiales de deux tenseurs symmetriques dans quelques cas d'anisotropie," Arch. Mech. Stosow., 23, No. 3, 431-444 (1977). G. F. Smith, "On isotropic function of symmetric tensors, skew-symmetric tensors and vectors," Int. J. Eng. Sci., 9, No. i0, 899-916 (1971).

Symbolic method in invariant theory

A symbolic method based on an extension of the straightening algorithm is developed for the representation of joint invariants of symmetric and skew-symmetric tensors. For skew-symmetric tensors, the method holds over infinite fields of arbitrary characteristic.

Complex parabolic subgroups of G 2 and nonlinear differential equations

Nonlinear ordinary differential equations with superposition formulas corresponding to the exceptional Lie group G2ℂ and its two maximal (complex) parabolic subgroups are determined. The G2-invariance of a third-order skewsymmetric tensor is exploited. The obtained ODEs have polynomial nonlinearities of order 2 in one case and of order 4 in the other.

Symmetry operators for neutrino and Dirac fields on curved spacetime

We characterize tensorially all first-order differential operators whose commutator with the massless Dirac operator is proportional to it on a general curved background in terms of skew-symmetric tensors satisfying conformally invariant generalizations of the Killing-Yano equations. The same problem is also solved for the massive charged Dirac equation on a general curved background.

Damage Tensors and Tensors of Continuity in Stress Analysis

Abstract Starting from a third order skew-symmetric tensor of continuity to represent area vectors (bivectors) of Cauchy's tetrahedron in a damaged state, a second order damage tensor is found which has the diagonal form with respect to the considered coordinate system. The second part of the paper is concerned with the stresses in a damaged continuum. Introducing a linear operator of rank four a net-stress tensor is formulated. This tensor can be decomposed into a symmetric part and into an antisymmetric one, where only the symmetric part is equal to the net-stress tensor introduced by Rabotnov [7]. In view of the formulation of constitutive equations the non-symmetric property of the actual net-stress tensor is a disadvantage. Therefore, a pseudo-net-stress tensor is introduced, which is symmetric.

Supermanifold description of the BRS symmetries of skewsymmetric tensor gauge fields

The authors extend Tulczyjew's geometrical formulation of skewsymmetric tensor gauge fields as connections on generalised principal fibre bundles to the category of supermanifolds. Given a smooth d-dimensional manifold M and a k-form field on it, they construct a suitable supersmooth generalised principal fibre bundle P over a (d,2)-dimensional supermanifold M such that the BRS symmetries of the theory have a natural geometrical interpretation.

Geometric supergravity in D=11 and its hidden supergroup

In this paper we address two questions: the geometrical formulation of D = 11 supergravity and the derivation of the super Lie algebra it is based on. The solutions of the two problems are intimately related and are obtained via the introduction of the new concept of a Cartan integrable system described in this paper. The previously developed group manifold framework can be naturally extended to a Cartan integrable system manifold approach. Within this scheme we obtain a geometric action for D = 11 supergravity based on a suitable Cartan system. This latter turns out to be a compact description of a two-element class of supergroups containing, besides Lorentz J ab , translation P a and ordinary supersymmetry Q, the following extra generators: two- and five-index skew-symmetric tensors Z a1 a2 , Z a1… a5 and a further spinorial charge Q ′. Q ′ commutes with itself and everything J ab . It appears in the commutators of Q with P a , Z a1 a2 , Z a1 … a5.

On transversely isotropic functions of vectors, symmetric second-order tensors and skew-symmetric second-order tensors

On transversely isotropic functions of vectors, symmetric second-order tensors and skew-symmetric second-order tensors

Superfield formulation of skew-symmetric tensor gauge field theories

The Abelian gauge quantum field theories of skew-symmetric tensor fields are reviewed in the fremework of the superfield formalism previously proposed. The BRS invariance properties of those theories and the role of the secondary ghosts are discussed.

Relativistic wave equations for antisymmetric tensor gauge fields

Relativistic wave equations for totally skew-symmetric tensor gauge fields are regarded as generalized Maxwell equations. The spin content is determined for both the massive and massless case. In particular, we find that an antisymmetric tensor gauge field ${A}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}(x)$ represents a cosmological constant when massless while in the massive case it describes a spinless particle without violating the gauge invariance. This phenomenon is interpreted as a generalized Higgs mechanism.