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Can we consider string theory as a special type of field theory?

  1. Jul 13, 2013 #1
    The notion field of Quantum Field Theory is deduced from the combination of Quantum Mechanics and Special Relativity.The local characteristic of field is led from Cluster Decomposition Principle.
    String Theory is also a combination between Quantum Mechanics and Relativity Theory.Then I wonder whether the String Theory obeys Local Principle or not?Can we consider String Theory as a special type of Quantum Field Theory?
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  3. Jul 13, 2013 #2

    Simon Bridge

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    It's usually considered the other way around ... but why does it matter?
  4. Jul 13, 2013 #3
    I do not know whether String Theory obeys the Local Principle as Field Theory or not.If not,we can not consider String Theory as a special type of Field Theory.
  5. Jul 13, 2013 #4
    From Quantum Mechanics and Special Relativity Theory we deduce notion of field that based on two sub-notions:Locality and Broadeness(Local+Broaden=Field).Then does String notion base on the two notions of Locality and Broadeness or not?
  6. Jul 14, 2013 #5
    1) QFT does not equal special relativity + Quantum mechanics. There are nonrelativistic field theories and they are used in condensed matter physics. And there can be nonlocal field theories, a field theory is just quantum mechanics with infinite degrees of freedom (a field is defined throughout space time and for each point in spacetime there is a degree of freedom)

    2) No String theory is not a special kind of field theory, as people currently understand it at least. String perturbation theory is in the first quantized language, the creation and annihilation operators describe the dynamics of a single string, and do not correspond to creation operators for new strings. Thats not to say field theory does not play a role in string theory, 2d superconformal field theories arise which describe the worldsheet of the string. However in typical relativistic quantum field theory you have 1d field theories on the world line because particles are 0-dimensional

    A simple way that string theory is not a qft is that the string theory naturally includes the graviton, while the description of a massless, fundamental, spin two boson in QFT leads to a nonrenormalizable field theory (a linearized version of Einstein's gravity).

    3) There is a topic called string field theory, which attempts to describe string theory in a second quantized language (so more like field theory and less like relativistic QM). I suppose you can think of string field theory as a field theory with an infinite number of fields (similar to how the transition from QM to QFT is from a finite number of degrees of freedom to an infinite number of degrees of freedom). So string field theory is a generalization of field theory to describe strings.

    I can't emphasize this enough, there are nonlocal field theories, just right a term in a lagrangian like σ(x)θ(y)ψ(z) where x,y, and z are all different points. That interaction is nonlocal!
  7. Jul 14, 2013 #6
    As far as I know , String theory is not a field theory . We just don't know what string theory is so we study it using tools that come from field theory like faddeev popov ghosts and gauge fixing and functional integration. Gravity ,being nonrenormalizable,can't be described by a quantum field theory . Quantum field theories are just one way to derive theories whose S-matrix obey locality , unitarity and lorentz invariance . So if string theory is local , it doesn't have to be a field theory .
  8. Jul 14, 2013 #7


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    I think LBloom hit the nail on the head.
  9. Jul 14, 2013 #8
    So is String Theory being local or not?Can you point me some books saying about nonlocal quantum field theory?
  10. Jul 14, 2013 #9


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    Last edited: Jul 14, 2013
  11. Jul 15, 2013 #10


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    Quote from https://www.physicsforums.com/blog.php?b=3873 [Broken]

    "One surprising result is that first quantization of strings is enough, so one does not need second quantization of strings, called also string-field theory. Actually string-field theory exists as well, but it is not consistent, and almost nobody uses it. But still, first-quantized theory of strings is also a quantum field theory - more precisely conformal quantum field theory in 2 dimensions. But it does not mean that strings live in 2 dimensions, because they really live in 10 dimensions. But the 2-dimensional strings (actually 1-dimensional if we don't count time) that live in 10 dimensions are not the end of the story, because the theory contains also branes - objects having more than 2 stringy dimensions. These branes are not really fundamental, because they are only special configurations of classical 10-dimensional fields, while these 10-dimensional fields themselves are not fundamental. Despite of being non-fundamental, these classical 10-dimensional fields are actually quantum 10-dimensional fields, but nobody knows how to quantize them because, as I said, string-field theory is not consistent (and not even needed)."
    Last edited by a moderator: May 6, 2017
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