An Introduction To Kaluza Klein Theories

A comprehensive and impressive collection of original and translated papers by Kaluza, Klein, Einstein and others, carefully edited to place them in their historical and intellectual context.

Twenty-five years of Schladming Winter School 1. The Start Twenty-five years ago P. Urban had the idea of organizing a winter school in the Austrian mountains. The very concept of a school was not new: to bring physicists together in an environment which differs totally from the daily world of institutes and laboratories, to contrast hard classroom work in lectures by distinguished speakers with a relaxed atmosphere, to provide opportunities for entering newly developing fields and exchanging ideas, all this had already resulted in a few summer schools in southern Europe and the US. The idea of combining physics with skiing rather than swimming was, however, new. After some sampling by a few younger members of Ur ban's group, Schladming was selected as an appropriate place. At that time skiing was not very much developed here; there were few lifts, but a road to Hochwurzen and a regular bus service opened at least one longer track. The first meeting took place in a classroom of the local school, w here some 40 participants were squeezed into benches designed for children. In the next year we moved into the dining hall of a small inn, which does not exist any more (an attempt to serve beer during the lectures was stopped by the orga nizing committee). Only in later years did we find a permanent home here in the Stadtsaal.

Yi-Shi Duan (1927–2016) was one of the world-renowned pioneers in the study of gauge field theory and general relativity. Trained in the former Soviet Union, Prof. Duan returned to China in 1957 to work in Lanzhou University for 60 years. In 1963, he came up with a general co-variant form of the conservation law of the energy-momentum tensor in general relativity. In 1979, he suggested that the gauge potential could be decomposed, which has important implications to gauge field theory. He trained in China a big team of talents in theoretical physics. His contributions to theoretical physics in China have earned him praise from both Professor Shiing-Shen Chern and Professor Chen-Ning Yang. Contents: SU(2) Gauge Theory and Electrodynamics with N Magnetic Monopoles (Yi-Shi Duan and Mo-Lin Ge)Abelian Decomposition of QCD (Y M Cho)How Can We Understand Quark Confinement in Quantum Yang–Mills Theory? (Kei-Ichi Kondo)Asymmetrical Input-output Control in Cavity Quantum Electrodynamics (Yifu Zhu)Energy and Angular Momentum in Gravity Theories (Rong-Gen Cai and Li-Ming Cao)Gravitational Energy and the Gauge Theory Perspective (Chiang-Mei Chen and James M Nester)Energy-Momentum in General Relativity (Xiaoning Wu and Xiao Zhang)Introduction to Extra Dimensions and Thick Braneworlds (Yu-Xiao Liu)Appendices: Chronicle of Prof. Yi-Shi Duan's LifeChronicle of Prof. Yi-Shi Duan's Life (Chinese Version)List of Prof. Yi-Shi Duan's Publications Readership: Graduate students; researchers. Keywords: Yi-Shi Duan;Yang-Mills Theory;General Relativity;Modified Gravity;Gauge Potential Decomposition;Monopole;Energy-Momentum Tenor;Brane World Scenario;Conserved Charge;Cavity Quantum ElectrodynamicsReview: Key Features: Yi-Shi Duan was one of the world-renowned pioneers in the study of gauge field theory and general relativity in ChinaHe trained a big team of talents in theoretical physics in China, such as Mo-Lin Ge, Rong-Gen Cai, etc.His contributions to theoretical physics in China have earned him praise from both Professor S S Chern and Professor C N Yang

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Einstein's general theory of relativity can be a notoriously difficult subject for students approaching it for the first time, with arcane mathematical concepts such as connection coefficients and tensors adorned with a forest of indices. This book is an elementary introduction to Einstein's theory and the physics of curved space-times that avoids these complications as much as possible. Its first half describes the physics of black holes, gravitational waves and the expanding Universe, without using tensors. Only in the second half are Einstein's field equations derived and used to explain the dynamical evolution of the early Universe and the creation of the first elements. Each chapter concludes with problem sets and technical mathematical details are given in the appendices. This short text is intended for undergraduate physics students who have taken courses in special relativity and advanced mechanics.