I'm not very familiar about String theory but just curious. I wanted to know, in what sense are the strings of string theory different from quanta of relativistic fields (which we interpret as particles)? I'm looking for an answer that an self-taught student of quantum field theory and someone unfamiliar with the mathematical formalism of string theory can understand.
In quantum field theory, particles or field excitations are momentum eigenstates and therefore, delocalized. And hence, they are not point objects. Popular talks of string theory also suggest that strings too are extended objects. Then what is the difference between strings and particles (as learnt in quantum field theory).
A not-too-technical answer will be helpful.
Best Answer
Strings are not quanta. They are not excitations of something, they are the fundamental objects from which standard string theory starts building its model. In quantum field theory, particles only appear in the theory once it is quantized. The classical field theory corresponding to a QFT doesn't know anything about particles. In string theory, the classical model from which we start is the one of string moving freely in some high-dimensional target space.
Quantizing the movement of string in the target space then gives us quanta, which we interpret as excitations of the string and which we believe to correspond to the usual QFT particles in a low-energy effective regime. The strings of string theory therefore are much more analogous to the fields of quantum field theory than to particles in this technical sense.
However, string theory is not a quantum field theory, and this shows in the "stringy Feynman diagrams" it uses to compute perturbative string amplitudes. Here, one might start to think that the string becomes analogous to the particle because the diagrams simply are two-dimensional manifolds that look like "fattened Feynman diagrams", with string interaction corresponding to higher-genus 2D manifolds. However, there is additional data on this worldsheet that carries the information about the actual state we are scattering (a vertex operator), the string itself does not represent the scattered state while the particles in QFT certainly are the scattered states.
It is from this picture that one derives the intuition that it is the "extended nature" of the string that resolves the infinities of QFT - these 2D diagrams are smooth and do not lead to the same kind of infinities that we would need to renormalize as the ordinary Feynman diagrams, which are often thought of as the world lines of a point particle. But this doesn't mean that string theory is "replacing point particles by strings". String theory is truly a different kind of theory that only in low-energy effective regimes (which are usually still at ludicrously high energies from the usual QFT viewpoint) gives back ordinary QFT, where the stringy quanta can be described as the quanta of fields again.