Let (M,g) be a compact Riemannian manifold. The conformal class of g consists of all metrics g̃ = e2ug for any smooth function u. A central theme in conformal geometry is the study of properties that are common to all metrics in the same conformal class, and the understanding and classification of all the conformal classes. For this purpose it is often useful to be able to single out a unique re...

We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincaré accessory parameters. This provides the semiclassical four point vertex functio...

where ω is a closed 1-form. ω is uniquely determined by Ω and is called the Lee form of Ω. (M,Ω, ω) is called a locally conformal symplectic manifold. If Ω satisfies (1) then ω|Ua = d(ln fa) for all a ∈ A. If fa is constant for all a ∈ A then Ω is a symplectic form on M . The Lee form of the symplectic form is obviously zero. Locally conformal symplectic manifolds are generalized phase spaces o...

The wave functions of the Haldane-Rezayi paired Hall state have been previously described by a non-unitary conformal eld theory with central charge c = ?2. Moreover, a relation with the c = 1 unitary Weyl fermion has been suggested. We construct the complete unitary theory and show that it consistently describes the edge excitations of the Haldane-Rezayi state. Actually, we show that the unitar...

We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R × R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over V L ⊗ V R , where V L and V R are two vertex operat...

The wave functions of the Haldane-Rezayi paired Hall state have been previously described by a non-unitary conformal field theory with central charge c = −2. Moreover, a relation with the c = 1 unitary Weyl fermion has been suggested. We construct the complete unitary theory and show that it consistently describes the edge excitations of the Haldane-Rezayi state. Actually, we show that the unit...

We discuss QCD evolution equations for two and three particle correlation functions of quarks and gluon fields in a hadron which describe development of the momentum distribution of a parton system with a change of the wave length of a probe which resolves it. We show in a general case of two-particle correlators how the four-dimensional conformal algebra and the known pattern of conformal symm...

The wave functions of the Haldane-Rezayi paired Hall state have been previously described by a non-unitary conformal eld theory with central charge c = ?2. Moreover, a relation with the c = 1 unitary Weyl fermion has been suggested. We construct the complete unitary theory and show that it consistently describes the edge excitations of the Haldane-Rezayi state. Actually, we show that the unitar...

The thrust of this project was to evaluate commercial conformal encapsulation candidates for low cost aerospace applications. The candidate conformal coatings evaluated in this study included silicone elastomers, epoxies, and Parylenes with bi-layer or tri-layer designs. Properties characterized in this study included mobile ion permeation and moisture ingress resistance, interfacial adhesion v...