We test the method of infinitesimal unitary transformations recently introduced by Wegner on the Anderson single impurity model. It is demonstrated that infinitesimal unitary transformations in contrast to the Schrieffer Wolff transformation allow the construction of an effective Kondo Hamiltonian consistent with the established results in this well understood model. The main reason for this is...

In this article we will invetsigate the origin of central charges in the Poisson algebra of charges, which arise in dimensionally reduced theories describing black holes. In order to do this we will analyze the equations of motion arising from the dimensionally reduced EinsteinHilbert action with the ansatz of spherical symmetry. We will show that the equations of motion and the constraints, wh...

We show that any conformal field theory in d-dimensional Minkowski space, in a phase with spontaneously broken conformal symmetry and with the dilaton among its fields, can be rewritten in terms of the static gauge (d − 1)-brane on AdS(d+1) by means of an invertible change of variables. This nonlinear holographic transformation maps the Minkowski space coordinates onto the brane worldvolume one...

Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on gene...

By using the Lie’s invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schrödinger equations with variable coefficients. Starting from the equivalence generators we construct the differential invariants of order one. We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schrödinger equations whi...

Korn’s inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its tr...

Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent z = 1, none of the known variants of conformal invariance can act as its dynamical symmetry. In d = 1 spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras. The infinitesimal gene...

The study of spheres dates back to the first century in the book Sphaerica of Menelaus. Spherical trigonometry was thoroughly developed in modern form by Euler in his 1782 paper [?]. Spherical geometry in n-dimensions was first studied by Schläfli in his 1852 treatise, which was published posthumously in 1901 [?]. The most important transformation in spherical geometry, Möbius transformation, w...