We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized tomograms
. Some of the new tomograms may have interesting applications in quantum optical tomography.
Some non-linear generalizations of classical Radon tomography were recently introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the straight lines of the standard Radon map are replaced by quadratic curves (ellipses, hyperbolas, circ
les) or quadratic surfaces (ellipsoids, hyperboloids, spheres). We consider here the quantum version of this novel non-linear approach and obtain, by systematic use of the Weyl map, a tomographic encoding approach to quantum states. Non-linear quantum tomograms admit a simple formulation within the framework of the star-product quantization scheme and the reconstruction formulae of the density operators are explicitly given in a closed form, with an explicit construction of quantizers and dequantizers. The role of symmetry groups behind the generalized tomographic maps is analyzed in some detail. We also introduce new generalizations of the standard singular dequantizers of the symplectic tomographic schemes, where the Dirac delta-distributions of operator-valued arguments are replaced by smooth window functions, giving rise to the new concept of thick quantum tomography. Applications for quantum state measurements of photons and matter waves are discussed.
In this paper we analyse the structure of the BRST charge of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generato
rs. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.
We analyze the antiferromagnetic $text{SU}(3)$ Heisenberg chain by means of the Density Matrix Renormalization Group (DMRG). The results confirm that the model is critical and the computation of its central charge and the scaling dimensions of the fi
rst excited states show that the underlying low energy conformal field theory is the $text{SU}(3)_1$ Wess-Zumino-Novikov-Witten model.
We discuss some differences in the properties of both even and odd Fedosov and Riemannian supermanifolds.
We analyze from a general perspective all possible supersymmetric generalizations of symplectic and metric structures on smooth manifolds. There are two different types of structures according to the even/odd character of the corresponding quadratic
tensors. In general we can have even/odd symplectic supermanifolds, Fedosov supermanifolds and Riemannian supermanifolds. The geometry of even Fedosov supermanifolds is strongly constrained and has to be flat. In the odd case, the scalar curvature is only constrained by Bianchi identities. However, we show that odd Riemannian supermanifolds can only have constant scalar curvature. We also point out that the supersymmetric generalizations of AdS space do not exist in the odd case.
Generalizations of symplectic and metric structures for supermanifolds are analyzed. Two types of structures are possible according to the even/odd character of the corresponding quadratic tensors. In the even case one has a very rich set of geometri
c structures: even symplectic supermanifolds (or, equivalently, supermanifolds with non-degenerate Poisson structures), even Fedosov supermanifolds and even Riemannian supermanifolds. The existence of relations among those structures is analyzed in some details. In the odd case, we show that odd Riemannian and Fedosov supermanifolds are characterized by a scalar curvature tensor. However, odd Riemannian supermanifolds can only have constant curvature.
The vacuum structure is probed by boundary conditions. The behaviour of thermodynamical quantities like free energy, boundary entropy and entanglement entropy under the boundary renormalization group flow are analysed in 2D conformal field theories.
The results show that whereas vacuum energy and boundary entropy turn out to be very sensitive to boundary conditions, the vacuum entanglement entropy is independent of boundary properties when the boundary of the entanglement domain does not overlap the boundary of the physical space. In all cases the second law of thermodynamics holds along the boundary renormalization group flow.
