Exact solutions of ℂPn models
Harmonic maps theory include some examples of non linear field theories of physical interest, among which stationary axisymmetric electrovacuum Einstein equations. After a short review of such applications, we concentrate on the so called CPn models. This is a very nice example of an harmonic physical problem, about which much is known. In particular we discuss the energy spectrum and the space of parameters of exact solutions of these models on the Riemann sphere.
KeywordsHomotopy Class North Pole Riemann Sphere Instanton Solution Jacobi Field
Unable to display preview. Download preview PDF.
- (1).J. Eells and L. Lemaire “A Report on Harmonic Maps”, Bull. London Math. Soc. 10, 1–68 (1978).Google Scholar
- (2).C. Reina “On the Harmony of the Ernst Equation”, Proc. 3rd M. Grossmann Meeting — Shangai (1982) (in press).Google Scholar
- (3).J. Eeels and J.C. Wood “Harmonic Maps from Surfaces to complex Projective Spaces”, Adv. Math. 49, 217–263 (1983).Google Scholar
- (4).R. Catenacci, M. Cornalba e C. Reina “Classical Solutions of CPn non Linear σ-models. An Algebraic Geometrical Description”. Geometry and Physics (1984) (in press).Google Scholar
- (5).A.M. Din and W.J. Zakrzewsky:“General Classical Solution of CPn-l models”. Nucl. Phys. B174 (1980), 397.Google Scholar
- (6).S. Kobajashi and K. Nomitzu “Foundations of Differential Geometry”, Interscience N.Y. (1969).Google Scholar
- (7).P. Griffiths and J. Harris:“Principles of Algebraic Geometry”, Wiley & Sons, New York (1978).Google Scholar
- (8).R. Catenacci, M. Cornalba e C. Reina “On the Energy Spectrum and Parameter Spaces of Classical CPn models”. Commun.Math.Phys.89,375–386 (1983)Google Scholar
- (9).R. Catenacci and C. Reina: Algebraic Classification of CPn Instanton Solutions, Lett. Math. Phys. 5 (1981), 469–473.Google Scholar
- (10).R. Catenacci, M. Martellini and C. Reina: On the Energy Spectrum of CP2 Models, Phys. Lett. 115B, 461-2 (1982).Google Scholar
- (11).C. Reina: Algebraic Geometrical Methods in Field Theory: The Example of CPn models, Proceedings of the International Meeting on Geometry and Physics (Florence, 1982)-Geometry and Physics (1984) (In press).Google Scholar