Causality in string field theory

[Urs Schreiber]

Apparently in string field theory string fields commute if the _center of
mass_ of the strings is spacelike seperated, irrespective of the oscillation
and spatial extension of the string.

I haven't thought about this issue before, but Bert Schroer yesterday told
me that he thinks that this is somehow problematic and that he would rather
see 'string fields' commute when all points on two strings are strictly
spacelike seperated. He discusses this in math-ph/0402043 in the context of
what he calls 'string localized quantum fields', which seems to be a concept
very different from anything derivable from the Polyakov action.

I am not sure that I fully understand both the content of math-ph/0402043 as
well as Bert Schoer's concern about Polyakov string theory.

I have some links and an email by Bert Schroer here:

http://golem.ph.utexas.edu/string/archives/000338.html

I'd be grateful if anyone could comment on this issue.

[Barton Zwiebach]

My knowledge on the matter indicates that the
quoted statement by Urs is not believed to
be correct:

> Apparently in string field theory string fields commute if the center of
> mass of the strings is spacelike seperated, irrespective of the oscillation
> and spatial extension of the string.

I have not done work on this, but the last reference
I know is from Hata and Oda (hep-th/9608128), who cites
earlier work and claims that one gets a vanishing
commutator for open string fields $\Phi (X)$ and
$\Phi (\tilde X)$, when

$$\int d\sigma ( X (\sigma) -\tilde X (\sigma) )^2 > 0. $$

It does not suffice that the CM's be spacelike separated to
satisfy this inequality. If the strings are fully spacelike
separated (any two points, one on each string, are spacelike
separated), the inequality is satisfied.

For free open strings, one can write

$$ (X-\tilde X)(\sigma) = \delta x_0 + \sum_n \delta x_n \cos (n\sigma)$$

The inequality is then roughly

$$(\delta x_0)^2 + \sum_n (\delta x_n)^2 > 0 $$

which shows that spacelike separated CM's $(\delta x_0)^2 >0$
does not suffice.

Much of the causality questions have been studied
in the light-cone gauge. I am not clear about the
role of reparameterization invariance when statements
are made about covariant closed string fields.

Best, Barton.

==================
Barton Zwiebach
Professor of Physics

Center for Theoretical Physics
MIT 6-303
77 Massachusetts Ave.
Cambridge, MA 02139-4307

Office 617 253-4839
Fax 617 253-8674

[Robert C. Helling]

On Tue, 30 Mar 2004, Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote:

> Apparently in string field theory string fields commute if the _center of
> mass_ of the strings is spacelike seperated, irrespective of the oscillation
> and spatial extension of the string.

I think this refers to the papers by Dimock. IIRC there one considers
the infinite towers of fields contained in the string and quantises
them as free fields. Those then appear to be located at the centre of
mass. I don't think this is very physical as it treats the string as a
collection of pointlike fields and thus has no chance to capture the
finite extension of the string.

Robert


--
..oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo. oOo.oOo.oOo.oOo.oOo.oOo.oOo.oO
Robert C. Helling Department of Applied Mathematics and Theoretical Physics
University of Cambridge
print "Just another Phone: +44/1223/766870
stupid .sig\n"; http://www.aei-potsdam.mpg.de/~helling

[Urs Schreiber]

On Wed, 31 Mar 2004, Robert C. Helling wrote:

> On Tue, 30 Mar 2004, Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote:
>
> > Apparently in string field theory string fields commute if the _center of
> > mass_ of the strings is spacelike seperated, irrespective of the oscillation
> > and spatial extension of the string.
>
> I think this refers to the papers by Dimock.


Yes. That's what Bert Schroer referred to.


> I don't think this is very physical as it treats the string as a
> collection of pointlike fields and thus has no chance to capture the
> finite extension of the string.


I think this is in fact more or less Bert Schroer's point.
He regards the localization in equation (5) of math-ph/0402043
as a physically more reasonable condition for string-like objects.
But the semi-infinite rigid 'string-localized fields' in his
paper have of course little resemblance to the usual strings.

But apparently Dimock's work involves an oversimplification
while the truth is as indicated by Barton Zwiebach and hence
the criticism expressed in
http://golem.ph.utexas.edu/string/archives/000338.html
does not apply here.

[Urs Schreiber]

On Wed, 31 Mar 2004, Urs Schreiber wrote:

> But apparently Dimock's work involves an oversimplification
> while the truth is as indicated by Barton Zwiebach and hence
> the criticism expressed in
> http://golem.ph.utexas.edu/string/archives/000338.html
> does not apply here.


Bert Schroer has now given an answer at
http://golem.ph.utexas.edu/string/archives/000338.html#c000887 .

He writes

"Dimock's pointlike localization of canonical strings
(math-ph/0308007) is an accepted result within the mathematical
physics community (Dimock is a first rate mathematical physicist)."

[Urs Schreiber]

On Wed, 31 Mar 2004, Robert C. Helling wrote:

> On Tue, 30 Mar 2004, Urs Schreiber <Urs.Schreiber@uni-essen.de> wrote:
>
> > Apparently in string field theory string fields commute if the _center of
> > mass_ of the strings is spacelike seperated, irrespective of the oscillation
> > and spatial extension of the string.
>
> I think this refers to the papers by Dimock. IIRC there one considers
> the infinite towers of fields contained in the string and quantises
> them as free fields. Those then appear to be located at the centre of
> mass. I don't think this is very physical as it treats the string as a
> collection of pointlike fields and thus has no chance to capture the
> finite extension of the string.

I have emailed Dimock and asked him if he thinks that Martinec, Hata,
Oda and other's calculations are erroneous or if he thinks that they
make different assumptions about the nature and definition of
string field theory than Dimock himself does.

My suspicion was that
the method of second quantization that J. Dimock uses in section 4
of math-ph/0308007 is not equivalent to that which one obtaines
by for instance starting with the action <psi|Q|psi> and that this
explains why he gets the result that string fields commute iff their
centers of mass are spacelike seperated while everybody else gets
the result that they commute iff int ds (X1-X2)^2 > 0.

Now I have received an answer by J. Dimock, where he tells me that
he thinks that his results are indeed compatible with the other
results!

I am completely puzzled by this answer, because I don't see in
which sense the two claims can be non-contradictory. I have
asked him to help me to see what he means, but haven't received an
answer yet.

Does anyone have a clue what J. Dimock might have in mind?

(See also
http://golem.ph.utexas.edu/string/archives/000338.html#c000889
)