Intuitive meaning of string wavefunction?

[Sauron]

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 $$X^\nu(\sigma,\tau)$$ 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:

$$\Phi(X^\nu(\sigma,\tau))$$ 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).

 

[Demystifier]

The string wave function is constructed analogously to that in the Schrodinger picture of quantum field theory. It is
$$\Psi[X(\sigma);\tau) ,$$
i.e., it is a functional with respect to $$X^{\mu}(\sigma)$$ and a function with respect to $$\tau$$.
For some additional technical details with a possible interpretation see
http://arxiv.org/abs/hep-th/0512186
http://arxiv.org/abs/hep-th/0605250

See also
https://www.physicsforums.com/showthread.php?t=94494

 

[Demystifier]

Afther all the KG in first quantization has a clear meaning.

Not quite! It is not clear what is its probabilistic interpretation in terms of probability densities for particle positions. See e.g.
http://arxiv.org/abs/quant-ph/0609163

 

[Demystifier]

For the most recent insight see also
http://arxiv.org/abs/hep-th/0702060

 

[rtharbaugh1]

What is probability density in space-time? Doesn't probability depend on causality, and isn't causality dependent on an arrow of time? If you adopt any space-time model, don't particles become strings, and duration in time is length of the string? Then if you invoke probabilities, they must involve the worldsheet, and all the probable paths of the particle. Feynman showed that one must go on to include all possible paths. Then in space-time you have this worm-burrow shape, where the worm is the string and the burrow is its worldsheet. It is a frozen shape in spacetime, and by the very idea of spacetime, the arrow of time is no longer has a preferred direction.

I think we have to get all these terms straightened out, so that we do not try to apply terms from a 3-space 1-time metric to 4d spacetime. It is analogous to trying to ask how long an area is in plane geometry. The idea of long as a unique value does not apply to areas.

R.

 

[Robert100]

Just checking: Is this a mainstream view of the debate?

Not quite! It is not clear what is its probabilistic interpretation in terms of probability densities for particle positions. See e.g.
http://arxiv.org/abs/quant-ph/0609163

Thanks for bringing this article to my attention. I just started to look at it, but I wanted to ask the opinions of other expert readers here. Is Nikolic's discussion of quantum "myths" fairly in the mainstream? I don't see any warning signs to the contrary, but I want to make sure that these are reasonable analyses of problems interpreting QM , and not just a set of criticisms unique to the author. :grumpy:

"Quantum mechanics: Myths and facts" by H. Nikolic

Summary: A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.

Any thoughts would be appreciated. Thanks,


Robert