# B Reconciling QM with string theory

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1. May 28, 2018

### Sophrosyne

I am trying to read about and understand string theory. But in trying to understand how it reconciles with the world of quantum field theory and quantum mechanics, I am getting a little confused. How does the string move through and propagate through the quantum field?

Does string theory, for example, propose that there is only one field, the String field, in which the strings vibrate? And the different particles are just different vibrations of the string of this fundamental String field?

2. May 29, 2018

### Demystifier

That's a very good question, the explicit answer to which is not easy to find in the string literature.

The first thing one needs to know is that "string theory" is not one theory. There are at least 3 versions of the theory, namely
1) perturbative string theory
2) string field theory
3) M theory
2) String field theory is an attempt to formulate string theory as a "second quantized" theory, similar to that in the book Bjorken and Drell "2", Relativistic Quantum Fields. According to this theory, fundamental objects are certain string fields. If ordinary field is thought of as a function of the form $\Phi({\bf x},t)$, the string field is a functional of the form $\Phi[{\bf X}(\sigma);t)$ where $\sigma$ is a real parameter along the string. At large distances one can use an approximation ${\bf X}(\sigma)\approx {\bf x}$, which is why at low energies one can approximate string field theory with ordinary field theory. String field theory is well understood for bosonic strings, but this theory does not describe fermions so is not realistic. Unfortunately, string field theory is not well understood for more realistic superstrings. Most string theorists believe that string field theory is not the correct approach to describe string theory at the fundamental level.