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When you study in a book basic quantization of the string lagrangian you can see two basic ways.

On ne hand you can see the [tex]X^\nu(\sigma,\tau)[/tex] coordinates of the worldsheet as fields and to make canonical quantization with them. On the other hand there is teh polyakov path integral.

But none of these natural proposals answer, A.F.A.I.K . a very trivial question. Wich would be the probabilistic interpretation of an string wavefunction? In fact, which would be the actual wvefunction of the string?

I mean, for a point particle, we can give a wavefunction whose square is the probability of finding the particle at a give point. For an stringy object, i guess that maybe you could form some kind of functional of the worldsheet , i.e. something like:

[tex]\Phi(X^\nu(\sigma,\tau))[/tex] but which would be its interpretation? (or the actual form to begin with)

I know that there are string field theories. But they mainly are interested, as far as I understand them, in given some notational convenience for doing second quantization. That´s finebut before doing a QFT with the KG equation it wa necesary to have a proper understandin of the meaning of a relativistic wavefunction. Afther all the KG in first quantization has a clear meaning. I would like to know of somne know of these for the string (or if someone even bothers about such trivial questions).

On ne hand you can see the [tex]X^\nu(\sigma,\tau)[/tex] coordinates of the worldsheet as fields and to make canonical quantization with them. On the other hand there is teh polyakov path integral.

But none of these natural proposals answer, A.F.A.I.K . a very trivial question. Wich would be the probabilistic interpretation of an string wavefunction? In fact, which would be the actual wvefunction of the string?

I mean, for a point particle, we can give a wavefunction whose square is the probability of finding the particle at a give point. For an stringy object, i guess that maybe you could form some kind of functional of the worldsheet , i.e. something like:

[tex]\Phi(X^\nu(\sigma,\tau))[/tex] but which would be its interpretation? (or the actual form to begin with)

I know that there are string field theories. But they mainly are interested, as far as I understand them, in given some notational convenience for doing second quantization. That´s finebut before doing a QFT with the KG equation it wa necesary to have a proper understandin of the meaning of a relativistic wavefunction. Afther all the KG in first quantization has a clear meaning. I would like to know of somne know of these for the string (or if someone even bothers about such trivial questions).

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