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B Reconciling QM with string theory

  1. May 28, 2018 #1
    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. jcsd
  3. May 29, 2018 #2

    Demystifier

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    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
    Each of these versions provides a different answer to your question.

    1) Perturbative string theory is the best understood version of string theory. According to this theory, there are no fields at the fundamental level. There are only strings, which scatter according to the "first quantization" rules similar to that in the book Bjorken and Drell "1", Relativistic Quantum Mechanics. But once you calculate the scattering amplitude and make a low energy limit, you observe that the same scattering amplitude can be obtained by a certain field theory. This field theory is only an effective theory valid at low energies, not a fundamental theory. Fields are emergent in perturbative string theory, not fundamental. The problem with perturbative string theory is that it is almost certainly incomplete. Therefore any general conclusions such as the ones I've just made should not be taken too seriously.

    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.

    3) M theory is widely believed to be the most fundamental formulation of string theory. In principle, it should give the best answer to your question. Unfortunately, M theory is not very well understood. It is not even known what the fundamental objects in this theory are supposed to be. There is even no agreement what the "M" stands for. Therefore, at this moment, M theory does not provide a clear unambiguous answer to your question.
     
    Last edited: May 29, 2018
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