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String theory: fundemental properties of string

  1. Jan 19, 2010 #1
    In string theory, what are the fundemental properties of a string?

    Is the tension in the string a constant at all points on the string and the same in all strings?
    Is the string "labelled" with fields/spin/etc along its length?
    How about "velocity"? Is each 'bit' of the string labelled with a velocity, or is there only a world-sheet? (ie. can we distinquish between a worldsheet that is a cylinder, vs. a "rotating" cylinder with the same points in spacetime)

    Trying to find introductory papers, it looks like the strings have no properties besides tension ... which the action ends up being proportional to, so it is not even measureable. If the string really isn't "labelled" with any properties along its length, then it seems like a right handed neutrino and a left handed neutrino would have to have the same mass because the world sheet would look the same either way. What am I missing here?
     
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  3. Jan 19, 2010 #2

    arivero

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    Ok, think how do you solve the question in a worldline, ie in quantum mechanics of a particle. Now think that the string is a bunch of worldlines labeled by a parameter sigma.

    1) Internal labels coming from the representation theory of the gauge groups on the strings themselves SO(32) etc.
    2) the decomposition in spatial eigenstates, in the same way that you decompose the electron trajectories in an atom to build the chemical orbitals. But now you can have the equivalent of orbitals in the extra dimensions.
     
  4. Jan 20, 2010 #3

    tom.stoer

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    I think the properties of a string are somehow hidden due to te fact that you normally study a quantized string. But if you keep in mind that quantization starts with a Fourier decomposition it becomes clear that physically a classical string is a "standard" string with "local properties" such as vibration, velocity.

    Regarding handedness: I am not an expert but it's clear that deriving handedness is difficult: As fas as I know you need at minimum supersymmetry (to let the string represent a fermion) and you need an heterotic string where the right movers and the left movers on the string behave differently. I have to check how this is represented in other (non-heterotic) theories.
     
  5. Jan 20, 2010 #4
    But that would mean we have to choose ahead of time what 'particle' the string is. Instead we should be able to 'derive' what particle each mode of the string is, no?

    I'm not understanding what you mean here.
    If SO(32) has representations for all the particles, and there are still multiple energy spatial modes, that would mean an electron itself can have an infinite number of energy states. At the very least it seems to mean the modes themselves are not associated with different particles.

    When I look at things like:
    http://en.wikipedia.org/wiki/Superstrings#The_mathematics
    It looks like there are no labels for the strings besides the "momentum" of the string pieces. I don't see how the theory could distinguish between different chiralities in interactions.
     
    Last edited: Jan 20, 2010
  6. Jan 21, 2010 #5

    tom.stoer

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    Perhaps the picture is too simply: it is not one classical obejct "string" that appears as a particle, it's the Hilbert space (something like a Fock space) that has a representation where you can identify states (= particles) with certain properties.
     
    Last edited: Jan 21, 2010
  7. Jan 21, 2010 #6

    arivero

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    I say, forget first about strings!!!!!!!!!!!!!!!

    Most of your questions apply to point particles. How does a point particle label its velocity if it is an eigenstate of position, or reciprocally? How does the chirality of the particle appear in the equation of a particle moving along a worldline?

    If SO(32) has representations for all the particles, and there are still multiple energy spatial modes, that would mean an electron itself can have an infinite number of energy states. At the very least it seems to mean the modes themselves are not associated with different particles.

    The answers follow the line suggested my tom.

    One you have got the idea for point particles, the next step is to understand it for open strings. Consider the extremes of open strings. Compare, say, with hidrogen atom: two extremes joined by some entity. In the case of the atom the entity is a boson field, and the energy levels of the atom are different, but it moves in space with a given energy, spin, position etc.

    Now, finally, strings: populate the line between the two extremes and allow for a tension: you get vibrating excited states. The solutions will be the relativistic version of the harmonics of a string.

    Label the extremes. It was proven that, due to extra dimensions and quantisation of fermions, there are 2^(10/2) combinations of labels. (proven by Marcus and Sagnotti).
    This is actually a problem for superstrings: they have a lot of labels to choose from! Note that due to a duality, the labeling survives when you close the strings, the SO(32) then relates to E8xE8 in a convoluted way.
     
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