*Post by pirillo*I think ultimately (and even in the intermediate steps)]

the size of the string 1) does not matter 2) is Ill defined.

One first has to define what one means by string size.

1) Conceptually

This is another FAQ. The last time this came up was here:

http://groups.google.de/group/sci.physics.strings/msg/01c88b017e3ccc62?hl=de

The following was my reply at that time. (There is of course much room for

improving on that reply.)

*Post by pirillo*Well, I already said, that I'd been informed that the average length of a

string is infinity.

Yes, but by regularizing (normal ordering) the observable which measures the

size of the string, one obtains a finite value which is physically very

interesting, since it can be related to black hole entropy considerations.

I recall that you, mandro, have asked these questions before, and I think I

had answered most of them, for instance in the thread

http://groups.google.de/groups?selm=dec722c5.0303061133.1bf83085%40po...

But maybe I wasn't pointing you to enough literature. Anybody interested in

these questions should have a look at the very nice paper

Thibault Damour, Gabriele Veneziano:

Self-gravitating fundamental strings and black-holes

hep-th/9907030

and references given there, where the observable measuring the rms size of a

string is given in equations (2.9)-(2.11).

The idea is quite simple: The mean squared diameter of the string is the

average of (X-X_0)^2, taken over the worldsheet, where X_0 is the center of

mass coordinate. Now expand X in terms of worldsheet Fourier modes as usual

and then integrate over the worldsheet coordinates in order to average. The

result is (2.11), which says that the rms size is proportional to

\sum_{n=1}^\infty \frac{1}{n^2} (\alpha_{-n} \cdot \alpha_n + \alpha_n

\cdot \alpha_{-n}).

Clearly, when you take the expectation value of this guy in any string state

you'll get an infinite contribution from pulling the annihilators \alpha_n

through the creators \alpha_{-n}. This is a common quantum effect and is

removed by normal ordering. It has been argued that this infinite

contribution to the string's length has a proper physical meaning - but the

point is that the remaining finite part has, too.

In particular, the finite part is related to string/black hole

correspondence, which I have tried to review here:

http://golem.ph.utexas.edu/string/archives/000379.html .

In Paris I had a chance to look at Barton Zwiebach's new textbook on string

theory (my own copy has not arribed yet) and I saw that there, too, a very

nice summary of the string/black hole correspondence along the lines

summarized at the above link is given. So maybe mandro and others will

benefit from having a look at that book.

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*Post by pirillo*To some people string size may just be the value

of a coupling constant.

That's not quite right. The value of the coupling constant in 10D string

theory is related to the dilaton which again is related to the circumference

of an extra dimension.