On conformally invariant equation $$( - \Delta )^p u - K(x)u^{\tfrac{{N + 2p}}{{N - 2p}}} = 0$$ and its generalizationsand its generalizations

2001 ◽  
Vol 179 (1) ◽  
pp. 309-329 ◽  
Author(s):  
Guozhen Lu ◽  
Juncheng Wei ◽  
Xingwang Xu
Keyword(s):  
Invariant Equation ◽  
Conformally Invariant

Construction of dipole type singular solutions for a biharmonic equation with critical Sobolev exponent

2002 ◽  
Vol 2 (4) ◽  
Author(s):  
Sarni Baraket
Keyword(s):  
Fourth Order ◽  
Weak Solutions ◽  
Biharmonic Equation ◽  
Critical Sobolev Exponent ◽  
Singular Solutions ◽  
Invariant Equation ◽  
Conformally Invariant ◽  
Sobolev Exponent

AbstractIn this paper, we construct positive weak solutions of a fourth order conformally invariant equation on S

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

1969 ◽  
Vol 313 (1512) ◽  
pp. 71-82 ◽  
Keyword(s):  
Local Geometry ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Coordinate Singularity ◽  
Previous Solution ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric ◽  
Radial Variable

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

scholarly journals OFF-CRITICAL CURRENT ALGEBRAS

1995 ◽  
Vol 10 (12) ◽  
pp. 1717-1736 ◽  
Author(s):  
E. ABDALLA ◽  
M.C.B. ABDALLA ◽  
G. SOTKOV ◽  
M. STANISHKOV
Keyword(s):  
Abelian Group ◽  
Critical Current ◽  
General Structure ◽  
Dimensional Algebra ◽  
Fermionic Model ◽  
Infinite Dimensional ◽  
Conformally Invariant ◽  
Current Algebras

We discuss the infinite-dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis on the structure of the consequent non-Abelian infinite-dimensional algebra generalizing W∞ to the case of a non-Abelian group. We prove that the pure left sector as well as the pure right sector of the thus-obtained algebra coincides with the conformally invariant case. The mixed sector is more involved, although the general structure seems to be near to being unraveled. We also find some subalgebras that correspond to Kac-Moody algebras. The constraints imposed by the algebras are very strong and, in the case of the massive deformation of a non-Abelian fermionic model, the symmetry alone is enough to fix the two- and three-point functions of the theory.

scholarly journals Einstein gravity as a 3D conformally invariant theory

2011 ◽  
Vol 28 (4) ◽  
pp. 045005 ◽  
Author(s):  
Henrique Gomes ◽  
Sean Gryb ◽  
Tim Koslowski
Keyword(s):  
Invariant Theory ◽  
Einstein Gravity ◽  
Conformally Invariant

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

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