Following the construction of the invariant integral and the scalar product for the quantum Euclidean group Eq(2), we obtained the full matrix elements of its unitary irreducible representations from SUq(2) by contraction and then derived the Planscherel measure.

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs on AdSd+1 and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the ...

This short review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the product form. The sigma-model approach and exact solutions are reviewed.

Let D be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On ZD we define a product and a coproduct, together with an internal product, that is, degree-preserving. With these operations ZD is a Hopf algebra, self-dual with respect to a scalar product which counts the number of pictures (in the sense of Zelevinsky) between two do...

We investigate the ground state of a free massless (pseudo)scalar field in 1+1– dimensional space–time. We argue that in the quantum field theory of a free massless (pseudo)scalar field without infrared divergences (Eur. Phys. J. C 24, 653 (2002)) the ground state can be represented by a tensor product of wave functions of the fiducial vacuum and of the collective zero–mode, describing the moti...

We investigate the ground state of a free massless (pseudo)scalar field in 1+1– dimensional space–time. We argue that in the quantum field theory of a free massless (pseudo)scalar field without infrared divergences (Eur. Phys. J. C 24, 653 (2002)) the ground state can be represented by a tensor product of wave functions of the fiducial vacuum and of the collective zero–mode, describing the moti...

Using an algorithm for computing the symmetric function Kronecker product of D-finite symmetric functions we find some new Kronecker product identities. The identities give closed form formulas for trace-like values of the Kronecker product. Introduction In the process of showing how the scalar product of symmetric functions can be used for enumeration purposes, Gessel [3], proved that this pro...

A pseudospectrum analysis has recently provided evidence of a potential generic instability black hole (BH) quasinormal mode (QNM) overtones under high-frequency perturbations. Such depends on the assessment size This is encoded in scalar product and its choice not unique. We address impact choice, founding it physical energy scales problem. The article organized three parts: basics, applicatio...