Bøger udgivet af Minkowski Institute Press

Neither general relativity (which revealed that gravity is merely manifestation of the non-Euclidean geometry of spacetime) nor modern cosmology would have been possible without the almost simultaneous and independent discovery of non-Euclidean geometry in the 19th century by three great mathematicians - Nikolai Ivanovich Lobachevsky, János Bolyai and Carl Friedrich Gauss (whose ideas were later further developed by Georg Friedrich Bernhard Riemann).This volume contains three works by Lobachevsky on the foundations of geometry and non-Euclidean geometry: "Geometry", "Geometrical investigations on the theory of parallel lines" and "Pangeometry". It will be of interest not only to experts and students in mathematics, physics, history and philosophy of science, but also to anyone who is not intimidated by the magnitude of one of the greatest discoveries of our civilization and would attempt to follow (and learn from) Lobachevsky's line of thought, helpfully illustrated by over 130 figures, that led him to the discovery.

This book is roughly divided in three parts. The first one is a general introduction to theories with extra dimensions and, more specifically, to brane worlds. Both old-fashioned topics (such as Kaluza-Klein theories) and more modern aspects (e.g. Large Extra Dimensions and Randall-Sundrum models) are discussed. The second and third parts (which we refer to as Part I and II respectively) are essentially two monographs. There, the reader is guided through the construction of the 4D effective field theory derived from higher dimensional (in particular five-dimensional and six-dimensional) models. Part I is devoted to the study of how the heavy Kaluza-Klein modes contribute to the low energy dynamics of the light modes. Part II concerns instead the analysis of the spectrum arising from non-standard compactifications of six-dimensional (supersymmetric) theories, involving a warp factor and conical defects in the internal manifold. Several applications of the above mentioned topics are discussed, providing an up to date overview of these subjects.