Second Order Perturbations in the Randall-Sundrum Infinite Brane-World Model

We discuss the non-linear gravitational interactions in the Randall-Sundrum single brane model. If we naively write down the 4-dimensional effective action integrating over the fifth dimension with the aid of the decomposition with respect to eigen modes of 4-dimensional d'Alembertian, the Kaluza-Klein mode coupling seems to be ill-defined. We carefully analyze second order perturbations of the gravitational field induced on the 3-brane under the assumption of the static and axial-symmetric 5-dimensional metric. It is shown that there remains no pathological feature in the Kaluza-Klein mode coupling after the summation over all different mass modes. Furthermore, the leading Kaluza-Klein corrections are shown to be sufficiently suppressed in comparison with the leading order term which is obtained by the zero mode truncation. We confirm that the 4-dimensional Einstein gravity is approximately recovered on the 3-brane up to second order perturbations.Comment: 15 pages, 2 figures, comment and reference added, typos correcte

Characterization of antibodies in sera of allergic individuals.

The introduction into an animal of a foreign substance, usually a natural macromolecule such as a protein, a polysaccharide or a conjugated lipid induces the production of globular serum proteins which possess the unique property of combining specifically with the foreign substance (1). These serum proteins are known as antibodies and the foreign substances responsible for their production are known as antigens. An animal or individual in whom antibodies have been formed is said to be immunized. These antibodies are produced either by natural exposure or injection of the antigen