the hydrogen atom is certainly not a “toy model”. The other examples you mention are important as long as they neglect the “minor details” only.
But feel free to call you model(s) whatever you like. They are certainly very important, otherwise you would not analyze them.

Take the time….it is worth it.

Cheers,

-cvj

Cheers,

-cvj

Sorry to say this, but you lost me after the first paragraph. I will print your reply out and save it until I am able to understand it, which may be a few years from now. I have not studied pendulum motion yet. I am still trying to fathom F=ma and sliding blocks, let alone Newton’s law of universal gravity. I am a real slow student.

Jacques wrote a nice post about the subcritical model you mention,
several years ago
http://golem.ph.utexas.edu/~distler/blog/archives/000206.html

Interesting indeed, but can we agree that this falls in the category of “toy model” ?

I was busy with other things, not ignoring you Wolfgang. I did not mean my short reply to be a slap in the face, which is how you seem to have taken it….It’s just that I have this job I get paid for and it takes me away from blogging from time to time so my answers are not always as immediate, long (or existent) as at other times!

Cheers!

-cvj

“In 1+1 dimensional noncritical string theory, there is also a linear dilaton background (varying in a spacelike direction). And there’s a “Tachyon wall,” preventing strings from penetrating the region of strong coupling. So one has an S-matrix, of sorts, for string coming in from the weakly-coupled region, bouncing off the wall, and returning to the weakly-coupled region.”

See? In that case you do have some notion of an S-matrix.

Jacques points out what the problem is with super-critical models using a linear dilatons in the post you link to:
“However, for supercritical strings, the theory is strongly-coupled either in the far future or in the far past. It’s not clear how one defines an S-matrix.”

Again, at this point I assume that I have completely misunderstood what Clifford
is doing, since he certainly knows all this much better than I do (by a factor of many gogols .

If you’re looking at old blog posts, you should see one by Jacques Distler, http://golem.ph.utexas.edu/~distler/blog/archives/000551.html.

The low-dimensional noncritical string theories are not controversial in the way the supercritical ones are. Give Clifford some credit.

I assume that I am just too stupid to understand what your are talking about.
The little I know is that cancellation of anomalies requires D=10 for superstrings
(and D=11 for M-theory).
In non-critical string theories one can construct some clever ways to cancel the anomalies with higher order corrections a la Eva Silverstein and I think Jaume Gouis found another construction.
But these methods appear unphysical (see Lubos’ comments).

But I amy have completely misunderstood your post, especially the part
> What people never tell you is that it is a complete overstatement to say that
> string theory can only live in 10 dimensions. This is just wrong.

-cvj

Sure. Well, you will have to deal with (or explain away) the anomalies and the way I see it, the case for super-symmetry is mostly gone.
It is a different story, of course, if you consider non-critical strings as toy models only.

I wish you good luck of course.

So how about we talk about physics now, folks? I’ve not too much interest in discussing the existence of other discussions on other physics on other blogs.

Cheers,

-cvj