The quantum bosonic string
Peter West · Cambridge University Press eBooks · 2012
Don't worry, I know you'll never understand it. Wittgenstein to Bertrand Russell, his Ph.D supervisor, after he had defended his Ph.D thesis The initial reaction of many people when told that the fundamental entities of Nature may be strings is the response: what is so special about strings? This attitude is a reflection of the unexciting or, perhaps, all too familiar nature of string-like objects that we encounter in everyday life. The string we are interested in here is different in two important respects to the more familiar violin string as unlike the latter it embodies the principles of relativity and quantum mechanics. In the previous chapter on the classical relativistic string we did see some interesting properties, but we did not, at first sight, encounter any properties that might lead one to expect that strings might provide an important element in a unified theory of physics. In fact, it is only when one quantises the relativistic string that it becomes apparent that such strings are magical objects. In some sense, they take to quantum mechanics like a duck to water. We shall see that just as classically the string can be viewed as an infinite collection of point particles, when quantised it can be thought of as an infinite set of quantum particles, each of which corresponds to an irreducible representation of the Poincaré group and so to a given spin. The range of spins is from zero to infinity, there being, in general, more than one particle of a given spin.