Ivancevic_Applied-Diff-Geom

40 Applied Differential Geometry: A Modern Introductionof hadron (subatomic particle which experiences the strong nuclear force)behavior. In particle–accelerator experiments, physicists observed that thespin of a hadron is never larger than a certain multiple of the square ofits energy. No simple model of the hadron, such as picturing it as a setof smaller particles held together by spring–like forces, was able to explainthese relationships. In 1968, theoretical physicist Gabriele Veneziano wastrying to understand the strong nuclear force when he made a startling discovery.He found that a 200–year–old Euler beta function perfectly matchedmodern data on the strong force. Veneziano applied the Euler beta functionto the strong force, but no one could explain why it worked.In 1970, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskindpresented a physical explanation for Euler’s strictly theoretical formula. Byrepresenting nuclear forces as vibrating, 1D strings, these physicists showedhow Euler’s function accurately described those forces. But even afterphysicists understood the physical explanation for Veneziano’s insight, thestring description of the strong force made many predictions that directlycontradicted experimental findings. The scientific community soon lostinterest in string theory, and the Standard Model, with its particles andfields, remained un–threatened.Then, in 1974, John Schwarz and Joel Scherk studied the messenger–like patterns of string vibration and found that their properties exactlymatched those of the gravitational force’s hypothetical messenger particle- the graviton. They argued that string theory had failed to catch on becausephysicists had underestimated its scope. This led to the developmentof bosonic string theory, which is still the version first taught to many students.The original need for a viable theory of hadrons has been fulfilled byquantum chromodynamics (QCD), the theory of Gell–Mann’s quarks andtheir interactions. It is now hoped that string theory (or some descendantof it) will provide a fundamental understanding of the quarks themselves.Bosonic string theory is formulated in terms of the so–called Polyakovaction, a mathematical quantity which can be used to predict how stringsmove through space and time. By applying the ideas of quantum mechanicsto the Polyakov action - a procedure known as quantization - one candeduce that each string can vibrate in many different ways, and that eachvibrational state appears to be a different particle. The mass the particlehas, and the fashion with which it can interact, are determined by the waythe string vibrates - in essence, by the ‘note’ which the string sounds. Thescale of notes, each corresponding to a different kind of particle, is termedthe spectrum of the theory. These early models included both open strings,