ИСТИНА

I. Volobuev Lecture course Introduction to General relativity and theories with extra space-time dimensions Lecture 1 A historical introduction: scalar gravity theories and the theory of general relativity. Introduction to general relativity. The equivalence principle. Chronogeometry. Curvilinear coordinates. Distances and time intervals. Galilean coordinates. Linear connection and covariant differentiation. Riemannian connection. Lagrangian and equations of motion for the gravitational field. Linearized theory. Lecture 2 Kaluza-Klein theories. Isolation of the physical degrees of freedom. Dimensional reduction of the zero mode sector. The problem of electric charge. Lecture 3 Spontaneous compactification. The choice of matter fields. Symmetric gauge fields. Equations of spontaneous compactification with symmetric gauge fields. Dimensional reduction and model building. Lecture 4 Large extra dimensions. Rubakov-Shaposhnikov example. ADD scenario. Randall-Sundrum model. The RS solution and its physical interpretation. The radion and the necessity of stabilization. Lecture 5 Phenomenology of the stabilized Randall-Sundrum model. Processes with Kaluza-Klein gravitons. Higgs-radion mixing and searches for the radion dominated state. Universal extra dimensions and processes with Kaluza-Klein excitations of the SM gauge bosons. Problem 1 Second variation Lagrangian and the linearized equations of motion of the gravitational field in an arbitrary background. Problem 2 Wave functions in the extra dimension for Kaluza-Klein modes of gravitational, scalar, vector and spinor fields in the unstabilized Randall-Sundrum model. Литература 1. Л.Д. Ландау, Е.М. Лифшиц. т. 2, Теория поля. Наука 1988. 2. А. Ходос. Теории Калуцы-Клейна: общий обзор УФН 146 647–654 (1985) 3. И.П. Волобуев, Ж.М. Моурао, Ю.А. Кубышин, Г. Рудольф. Размерная редукция симметричных калибровочных полей, модели Хиггса и спонтанная компактификация. ЭЧАЯ т. 20, N3, 561-627, 1989. 4. E.E. Boos, Y.A.Kubyshin, M.N. Smolyakov and I.P. Volobuev, Effective Lagrangians for physical degrees of freedom in the Randall- Sundrum model, Class. Quant. Grav. 19 (2002) 4591 5. Э.Э. Боос, В.Е. Буничев, И.П. Волобуев, М.Н. Смоляков, Геометрия, физика и феноменология модели Рэндалл-Сундрума. ЭЧАЯ т. 43(1), стр. 82-155, 2012.