The Casimir forces on two parallel plates in conformally flat de Sitter background due to conformally coupled massless scalar field satisfying mixed boundary conditions on the plates is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries. Different cosmological ...

Using the effective potential, the large-N nonlinear O(N) sigma model with the curvature coupled term is studied on S 2 × R 1. We show that, for the conformally coupled case, the dynamical mass generation of the model in the strong-coupled regime on R 3 takes place for any finite scalar curvature (or radius of the S 2). If the coupling constant is larger than that of the conformally coupled cas...

C Elementary and special functions (search also class L5 ) C1 Integer-valued functions (e.g., factorial, binomial coefficient, permutations, combinations, floor, ceiling) C06GXFP Factorizes a positive integer n as n = n1 × n2. This routine may be used in conjunction with C06MCFP D Linear Algebra D1 Elementary vector and matrix operations D1a Elementary vector operations D1a1 Set to constant D1a...

Polymeric molds of the layer-by-layer photonic crystal can be economically synthesized with a microtransfer molding technique. The refractive indices of these molds are low, preventing formation of a photonic bandgap. We find that such molds can be conformally coated with higher-index material. Photonic band calculations find structures in which conformally coated layer-by-layer molds have comp...

In this paper we provide a complete characterization of fully nonlinear conformally invariant differential operators of any integer order on R, which extends the result proved for operators of the second order by A. Li and the first named author in [38]. In particular we prove existence and uniqueness of a family of tensors (suitably invariant under Möbius transformations) which are the basic b...

Using a formulation of QCD2 as a perturbed conformally invariant theory involving fermions, ghosts, as well as positive and negative level Wess-Zumino-Witten fields, we show that the BRST conditions become restrictions on the conformally invariant sector, as described by a G/G topological theory. By solving the corresponding cohomology problem we are led to a finite set of vacua. For G = SU(2) ...

The study of weakly symmetric and weakly projective symmetric manifold were initiated by Tamassy and Binh in 1989. Later on several authors studied weakly symmetric Riemannian manifold and analogous structures, viz. Weakly Ricci symmetric, weakly projective symmetric and weakly conformally symmetric Riemannian manifolds. At first we cited examples of weakly symmetric Riemannian manifolds. Next ...

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful static cylindrically symmmetric distributions of matter, smoothly matched to Levi-Civita vacuum spacetime. It is shown that the conformally flat solution with equal principal stresses represents an incompressible fluid. It is also proved that any conformally flat c...

The Casimir effect due to conformally coupled bulk scalar fields on background of conformally flat brane-world geometries is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy-momentum tensor and vacuum forces acting on boundaries. The special case of the AdS bulk is considered and the application to the Randall-Su...