String theory: fundemental properties of string

In summary, the fundamental properties of a string in string theory include tension, velocity, and internal labels represented by gauge groups. The string can be viewed as a series of worldlines labeled by a parameter sigma. However, the properties of a string may be hidden in the quantized version. Handedness and different energy states can be derived from the string's modes. The Hilbert space of the string can be seen as a Fock space where states represent particles with certain properties. The string's properties can be understood by comparing it to the extremes of an open string and the energy levels of a hydrogen atom. Superstrings have a large number of labels to choose from due to extra dimensions and quantization of fermions.
  • #1
JustinLevy
895
1
In string theory, what are the fundamental 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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  • #2
JustinLevy said:
In string theory, what are the fundamental 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"?

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.

JustinLevy said:
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?

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.
 
  • #3
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.
 
  • #4
arivero said:
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.
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?

arivero said:
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.
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.
 
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  • #5
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.
 
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  • #6
JustinLevy said:
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 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.
 

1. What is string theory?

String theory is a theoretical framework in physics that attempts to reconcile the currently known laws of physics, including quantum mechanics and general relativity. It proposes that the fundamental building blocks of the universe are not particles, but tiny, one-dimensional strings that vibrate at different frequencies.

2. How does string theory explain the fundamental properties of strings?

String theory posits that the fundamental properties of strings are determined by their length, tension, and the way they vibrate. The different vibrational patterns of strings give rise to the different particles and forces in the universe.

3. What is the significance of extra dimensions in string theory?

String theory requires the existence of extra dimensions beyond the three dimensions of space and one dimension of time that we experience. These extra dimensions are believed to be curled up and very small, and they are necessary for the mathematical consistency of the theory.

4. Is there any experimental evidence for string theory?

Currently, there is no experimental evidence for string theory. Due to the incredibly small scale at which strings vibrate, it is not possible to directly observe them with current technology. However, string theory has made many predictions that are consistent with known physical laws and has the potential to explain phenomena that are not yet understood.

5. What are some of the challenges facing string theory?

One of the major challenges of string theory is that it currently cannot be tested experimentally. Additionally, the theory is complex and requires advanced mathematical concepts, making it difficult to understand and work with. There are also ongoing debates and controversies within the scientific community about the validity and usefulness of string theory as a unifying theory of physics.

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