Weyl invariance and the origins of mass

By a uniform and simple Weyl invariant coupling of scale and matter fields, we construct theories that unify massless, massive, and partially massless excitations. Masses are related to tractor Weyl weights, and Breitenlohner–Freedman stability bounds in anti de Sitter amount to reality of these weights. The method relies on tractor calculus – mathematical machinery allowing Weyl invariance to be kept manifest at all stages. The equivalence between tractor and higher spin systems with arbitrary spins and masses is also considered.     

Superradiant spin-flip radiative emission of a spin-polarized free-electron beam

Radiative emission from the magnetic moments of the spins of an electron beam has never been observed directly, because it is fundamentally much weaker than the electric charge emission. We show that the detectivity of spin-flip and combined spin-flip-cyclotron-resonance-emission radiation can be substantially enhanced by operating with ultrashort spin-polarized electron beam bunches under conditions of superradiant (coherent) emission. The proposed superradiant spin-flip radiative emission scheme can be used for noninvasive diagnostics of polarized electron or positron beams. Such beams are of relevance in important scattering experiments off nucleons in nuclear physics and off magnetic targets in condensed matter physics.     

Einstein metrics in projective geometry

It is well known that pseudo–Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined projectively invariant differential equation. This equation is a special case of a so-called first Bernstein–Gelfand–Gelfand (BGG) equation. The general theory of such equations singles out a subclass of so-called normal solutions. We prove that non-degenerate normal solutions are equivalent to pseudo–Riemannian Einstein metrics in the projective class and observe that this connects to natural projective extensions of the Einstein condition.     

Conformally Invariant Powers of the Laplacian, <Emphasis Type="Italic">Q</Emphasis>-Curvature,and Tractor Calculus

 We describe an elementary algorithm for expressing, as explicit formulae in tractor calculus, the conformally invariant GJMS operators due to C.R. Graham et alia. These differential operators have leading part a power of the Laplacian. Conformal tractor calculus is the natural induced bundle calculus associated to the conformal Cartan connection. Applications discussed include standard formulae for these operators in terms of the Levi-Civita connection and its curvature and a direct definition and formula for T. Branson's so-called Q-curvature (which integrates to a global conformal invariant) as well as generalisations of the operators and the Q-curvature. Among examples, the operators of order 4, 6 and 8 and the related Q-curvatures are treated explicitly. The algorithm exploits the ambient metric construction of Fefferman and Graham and includes a procedure for converting the ambient curvature and its covariant derivatives into tractor calculus expressions. This is partly based on [12], where the relationship of the normal standard tractor bundle to the ambient construction is described. Received: 24 January 2002 / Accepted: 1 November 2002 Published online: 18 February 2003 Communicated by P. Sarnak     

An analysis of stimulated longitudinal electrostatic bremsstrahlung in a free-electron laser structure

An analysis of stimulated emission of radiation by an electron beam passing through a periodic longitudinal electrostatic field is presented, and its use in a free-electron laser structure is discussed. The analysis is based on a coupled-mode calculation of the interaction between a waveguided electromagnetic mode and an electron-beam plasma with finite cross section. The dispersion equation derived applies to the collective as well as the single electron regime. This research is supported in part by AFOSR Grant, 77-3445.