On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian k , with the property that ( k , B) is formally self-adjoint. These boundary problems are used to construct conformally invariant nonlocal operators on the boundary Σ, generalizing the conformal Dirichlet-to-Robin operator, with principal par...

In the present paper a global conformal invariant Y of a closed initial data set is constructed. A spacelike hypersurface Σ in a Lorentzian spacetime naturally inherits from the spacetime metric a differentiation De, the so-called real Sen connection, which turns out to be determined completely by the initial data hab and χab induced on Σ, and coincides, in the case of vanishing second fundamen...

Momentum space Ward identities are derived for the amputated n-point Green’s functions in 3 + 1 dimensional non-relativistic conformal field theory. For n = 4 and 6 the implications for scattering amplitudes (i.e. on-shell amputated Green’s functions) are considered. Any scale invariant 2-to-2 scattering amplitude is also conformally invariant. However, conformal invariance imposes constraints ...

To leading order in CX~ ( Q2), conformal symmetry specifies the eigensolutions of the evolution equation for meson distribution amplitudes, the wavefunctions which control large-momentum-transfer exclusive mesonic processes in &CD. We find that at next to leading order, the eigensolutions in various field theories depend on the regularization scheme, even for zero p-function. This is contrary t...

In the framework of perturbative QCD at large Q and low x, the conformal (global) group of transformations in the transverse coordinate space plays a crucial role. Indeed Lipatov and his collaborators [1] have derived the master equation for the derivative of the gluon structure function with respect to x by resuming the leading ( αs ( Q̄ ) log(1/x) )n terms at fixed αs ( Q̄ ) . This derivative i...

In this note we study the problem of conformally flat structures bounding conformally flat structures and show that the eta invariants give obstructions. These lead us to the definition of an Abelian group, the conformal cobordism group, which classifies the conformally flat structures according to whether they bound conformally flat structures in a conformally invariant way. The eta invariant ...

The Wünsch’s calculus for conformal Riemannian invariants is reformulated and essentially generalized to all parabolic geometries. Our approach is based on the canonical Cartan connections and the Weyl connections underlying all such geometries. The differential invariants for various geometric structures are the core ingredients for numerous applications both in geometry and geometric analysis...