# Strings = no infinities

1. Mar 22, 2012

### julian

I believe in LQG where the theory itself regularises itself (quantised volumes).....string theory is supposed to account for infinities too cus the interaction is smeared over extended objects rather than point particles....

First of all interactions dont occur at points in perturbative quantum gravity in the same sense of Fermi theory.

In string theory we take a step back in that strings do interact directly as in Fermi theory.

Second, so what if it is extended objects that interct??...say an extended object interacts with another extended object say at n points - doesnt that just say the UV divergence will be a power of n times greater than that for point particle interactions just divided by n??

Probably a stupid question...Im bit tired. cats among pigeons.

Last edited: Mar 22, 2012
2. Mar 23, 2012

### clamtrox

Why do you think an extended object is a clump of N point-like objects? Isn't the whole point of extended objects that they're not?

Now, I don't really know anything about string theory, so I can't really comment on how this works. It seems a little puzzling to me too that having one extended dimension immediately solves this problem. After all, the cross section is still point-like perpendicular to the string.

3. Mar 23, 2012

### marcus

Actually I don't think Julian was suggesting that (extended object = finite number of point objects).

The example was two extended objects that INTERACT at a finite number of points.

I think that's how it has to be if (in the math formulation of the theory) interaction is treated as occurring at discrete points. Just my guess, hopefully J. will clear it up for you. BTW I was impressed by the recent discussion in Relativity forum https://www.physicsforums.com/showthread.php?t=587239 involving several people and think it might relate to the topic here. I post the link just in case it does.

Last edited: Mar 23, 2012
4. Mar 23, 2012

### julian

I did mean to extend from N to infinty. I think I was being a bit frivolous. I think you draw out the world sheets of two interacting strings and then note that you cant identify a single point of inetraction.

5. Mar 23, 2012

### Mark M

Hi,

Remember, standard particle interactions work fine at zero sitance. The problem comes when you introduce gravity.

Gravity must be transmitted on quantum scales by a particle known as a graviton, so that particle interactions with gravity can be mathematically studied and understood.

When gravitons interact with particles at zero distance, as shown by the standard models attempt to include them, everything caves in. The equations break down into ultraviolet divergances, and infinities arise.

But in string theory, the graviton is represented by a closed loop string, allowing it to interact with particles at greater than zero distance, which elimnates any mathematical breakdowns, and allows for a coherant theory of quantum gravity. But remember: String theory's goal has never been to unify to provide a quantum description of gravity. But John Schwarz showed that it could, which made it much more attractive. Though, string theory seeks to unify all forces and provide a theory of everything - unlike other theories of QG which deal purely with gravity.

Last edited: Mar 23, 2012