scholarly journals Mixed Symmetry-Tipe (k,1) Massless Tensor Fields. Consistent Interactions Of Dual Linearized Gravity

2012 ◽  
Vol 56 (1) ◽  
pp. 106-111
Author(s):  
C. Bizdadea ◽  
S. O. Saliu ◽  
M. Toma
Keyword(s):  
Master Equation ◽  
Young Diagram ◽  
Tensor Field ◽  
Local Cohomology ◽  
Tensor Fields ◽  
Linearized Gravity ◽  
Mixed Symmetry

AbstractA particular case of interactions of a single massless tensor field with the mixed symmetry corresponding to a two-column Young diagram (k,1) with k=4, dual to linearized gravity in D=7, is considered in the context of: self-couplings, cross-interactions with a Pauli-Fierz field, cross-couplings to purely matter theories, and interactions with an Abelian 1-form. The general approach relies on the deformation of the solution to the master equation from the antifield-BRST formalism by means of the local cohomology of the BRST differential.

Consistent Interactions Involving Dual Formulations of Linearized Gravity in Terms of Massless Tensor Fields with the Mixed Symmetry (k,1)

2011 ◽  
Author(s):  
C. Bizdadea ◽  
E. M. Cioroianu ◽  
M. T. Miaută ◽  
S. O. Saliu ◽  
S. C. Săraru ◽  
...  
Keyword(s):  
Tensor Fields ◽  
Linearized Gravity ◽  
Mixed Symmetry

Polarization tensor in de Sitter gauge gravity

2021 ◽  
pp. 2150035
Author(s):  
R. Raziani ◽  
M. V. Takook
Keyword(s):  
Tensor Field ◽  
Vector Fields ◽  
Polarization Tensor ◽  
De Sitter ◽  
Field Equations ◽  
Tensor Fields ◽  
Sitter Group ◽  
Generalized Polarization ◽  
Mixed Symmetry ◽  
Symmetry Rank

The gauge theory of the de Sitter group, [Formula: see text], in the ambient space formalism has been considered in this paper. This method is important to construction of the de Sitter super-conformal gravity and Quantum gravity. [Formula: see text] gauge vector fields are needed which correspond to [Formula: see text] generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equations of these vector fields have been obtained. The gauge vector field solutions are recalled. By using these solutions, the spin-[Formula: see text] gauge potentials has been constructed. There are two possibilities for presenting this tensor field: rank-[Formula: see text] symmetric and mixed symmetry rank-[Formula: see text] tensor fields. To preserve the conformal transformation, a spin-[Formula: see text] field must be represented by a mixed symmetry rank-[Formula: see text] tensor field, [Formula: see text]. This tensor field has been rewritten in terms of a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, [Formula: see text], and tensor polarization of rank-2, [Formula: see text], which can be used in the gravitational wave consideration. There is a certain extent of arbitrariness in the choice of this tensor and we fix it in such a way that, in the limit, [Formula: see text], one obtains the polarization tensor in Minkowski spacetime. It has been shown that under some simple conditions, the spin-[Formula: see text] mixed symmetry rank-[Formula: see text] tensor field can be simultaneously transformed by unitary irreducible representation of de Sitter and conformal groups ([Formula: see text]).

scholarly journals COHOMOLOGICAL BRST ASPECTS OF THE MASSLESS TENSOR FIELD WITH THE MIXED SYMMETRY (k,k)

2004 ◽  
Vol 19 (27) ◽  
pp. 4579-4619 ◽  
Author(s):  
COSTIN-CĂTĂLIN CIOBÎRCĂ ◽  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
SOLANGE-ODILE SALIU
Keyword(s):  
Irreducible Representation ◽  
Young Diagram ◽  
Cohomology Group ◽  
Tensor Field ◽  
Mixed Symmetry ◽  
Brst Cohomology ◽  
Invariant Characteristic

The main BRST cohomological properties of a free, massless tensor field that transforms in an irreducible representation of GL(D,ℝ), corresponding to a rectangular, two-column Young diagram with k>2 rows are studied in detail. In particular, it is shown that any nontrivial co-cycle from the local BRST cohomology group H(s|d) can be taken to stop either at antighost number (k+1) or k, its last component belonging to the cohomology of the exterior longitudinal derivative H(γ) and containing nontrivial elements from the (invariant) characteristic cohomology H inv (δ|d).

DUAL LINEARIZED GRAVITY COUPLED TO BF-TYPE TOPOLOGICAL FIELD THEORIES IN D = 7

2012 ◽  
Vol 27 (24) ◽  
pp. 1250137 ◽  
Author(s):  
CONSTANTIN BIZDADEA ◽  
SOLANGE-ODILE SALIU ◽  
LIGIA STANCIU-OPREAN
Keyword(s):  
Tensor Field ◽  
Coupled Model ◽  
Field Theories ◽  
Linearized Gravity ◽  
Gauge Transformations ◽  
Mixed Symmetry ◽  
Topological Field ◽  
Gauge Structure ◽  
Deformation Procedure ◽  
Maximal Field

All consistent interactions in D = 7 that can be added to one of the dual formulations of linearized gravity via a massless tensor field with the mixed symmetry (4, 1) and an Abelian BF theory with a maximal field spectrum are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques. Among the striking features of the coupled model, we mention that the gauge transformations of all fields are deformed and the main ingredients of the gauge structure are strongly modified during the deformation procedure.

GAUGE FIXING FOR LINEARIZED GRAVITY AND ANTISYMMETRIC TENSOR FIELDS

1990 ◽  
Vol 05 (11) ◽  
pp. 2145-2154
Author(s):  
DEBASHIS GANGOPADHYAY
Keyword(s):  
Tensor Field ◽  
Antisymmetric Tensor ◽  
Projection Operators ◽  
Tensor Fields ◽  
Linearized Gravity ◽  
Longitudinal Modes ◽  
Covariant Derivatives ◽  
Antisymmetric Tensor Field ◽  
Gauge Fixing

Using the functional stochastic scheme, the gauge fixing term for linearized gravity is shown to be related to longitudinal modes within the framework of the usual set of momentum projection operators. A similar analysis is done for non-Abelian antisymmetric tensor field by replacing derivatives with covariant derivatives in all relevant equations and by constructing suitable operators for projecting out transverse and longitudinal modes.

scholarly journals New Results On Consistent Coupling Between BF Models And Dual Linearized Gravity

2012 ◽  
Vol 56 (1) ◽  
pp. 100-105
Author(s):  
C. Bizdadea ◽  
S. O. Saliu ◽  
L. Stanciu-Oprean
Keyword(s):  
Tensor Field ◽  
Linearized Gravity ◽  
Mixed Symmetry ◽  
Field Spectrum ◽  
Alternative Description ◽  
Gravity Theories ◽  
Maximal Field

AbstractGiven the recent renewed interest in alternative description of gravity theories in terms of topological BF models (possibly with extra-constraints) as well as in dual formulations of linearized gravity (DFLG), all consistent interactions in D=6 involving an Abelian BF model with a maximal field spectrum and the DFLG via a massless tensor field with the mixed symmetry of the type (3,1) are considered.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

scholarly journals A Yang–Mills Theory in Loop Space and Chapline–Manton Coupling

1997 ◽  
Vol 12 (02) ◽  
pp. 111-119 ◽  
Author(s):  
Shinichi Deguchi ◽  
Tadahito Nakajima
Keyword(s):  
Field Theory ◽  
Local Field ◽  
Loop Space ◽  
Tensor Field ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Yang Mills ◽  
Local Field Theory ◽  
Antisymmetric Tensor Field ◽  
Chern Simons

We consider a Yang–Mills theory in loop space with the affine gauge group. From this theory, we derive a local field theory with Yang–Mills fields and Abelian antisymmetric and symmetric tensor fields of the second rank. The Chapline–Manton coupling, i.e. coupling of Yang–Mills fields and a second-rank antisymmetric tensor field via the Chern–Simons three-form is obtained systematically.

scholarly journals Consistent Interactions in Terms of the Generalized Fields Method

1997 ◽  
Vol 12 (24) ◽  
pp. 4387-4397 ◽  
Author(s):  
Ömer F. Dayi
Keyword(s):  
Master Equation ◽  
Gauge Field ◽  
Tensor Field ◽  
General Scheme ◽  
Antisymmetric Tensor ◽  
Four Dimensions ◽  
Bf Theory ◽  
Free Theory ◽  
Antisymmetric Tensor Field

The interactions which preserve the structure of the gauge interactions of the free theory are introduced in terms of the generalized fields method for solving the Batalin–Vilkovisky master equation. It is shown that by virtue of this method the solution of the descent equations resulting from the cohomological analysis is provided straightforwardly. The general scheme is illustrated by applying it to the spin 1 gauge field in three and four dimensions, to free BF theory in 2D, and to the antisymmetric tensor field in any dimension. It is shown that it reproduces the results obtained by cohomological techniques.

scholarly journals Computational Algorithm for Covariant Series Expansions in General Relativity

2018 ◽  
Vol 173 ◽  
pp. 03021 ◽  
Author(s):  
Ivan Potashov ◽  
Alexander Tsirulev
Keyword(s):  
Tensor Field ◽  
Computational Algorithm ◽  
Series Expansions ◽  
Tensor Fields ◽  
Normal Coordinates ◽  
Covariant Derivatives ◽  
Taylor Polynomials ◽  
Real Analytic ◽  
Derivatives Of ◽  
Torsion Free

We present a new algorithm for computing covariant power expansions of tensor fields in generalized Riemannian normal coordinates, introduced in some neighborhood of a parallelized k-dimensional submanifold (k = 0, 1, . . .< n; the case k = 0 corresponds to a point), by transforming the expansions to the corresponding Taylor series. For an arbitrary real analytic tensor field, the coefficients of such series are expressed in terms of its covariant derivatives and covariant derivatives of the curvature and the torsion. The algorithm computes the corresponding Taylor polynomials of arbitrary orders for the field components and is applicable to connections that are, in general, nonmetric and not torsion-free. We show that this computational problem belongs to the complexity class LEXP.

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