Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Inclusion of information about external particles to calculate scattering amplitudes

+ 4 like - 0 dislike
438 views

In this (schematic) equation to calculate the scattering amplitude A by integrating over all possible world sheets and lifetimes of the bound states

$$ A = \int\limits_{\rm{life time}} d\tau \int\limits_{\rm{surfaces}} \exp^{-iS} \Delta X^{\mu} (\sigma,\tau)$$

the information about the incoming and outgoing particles is still missing. It has to be inserted by hand by including additional multiplicative factors (vertex operators)

$$ \prod\limits_j e^{ik_{j_\mu} X^{\mu}(z_j)}$$

into the integrand as Lenny Susskind explains at about 1:18 min here. But he does not derive the fact that the information about the external particles can (or has to) be included by these additional multiplicative factors like this, he just writes it down.

Of course I see that these factors represent a particle with wave vector $k$, and $z$ is the location of injection (for example on the unit circle when conformally transforming the problem to the unit disk) over which has finally to be integrated too.

But I'd like to see a more detailed derivation of these vertex operators (do there exit other ones too that contain additional information about other conserved quantities apart from the energy and the momentum?) and how they go into the calculation of scattering amplitudes, than such "heuristic" arguments.

asked Jan 2, 2013 in Theoretical Physics by Dilaton (6,240 points) [ revision history ]
Can you review the link, please? It seems to be talking about other matters at 1:18.

This post imported from StackExchange Physics at 2014-03-12 15:28 (UCT), posted by SE-user Sklivvz
Thanks a lot for catching this @Sklivvz, I linked to the wrong course ... Now it should be correct.

This post imported from StackExchange Physics at 2014-03-12 15:28 (UCT), posted by SE-user Dilaton

1 Answer

+ 1 like - 0 dislike

Jeff Harvey said this on Mathoverflow which is a good enough starting point for a CW answer even though I'd be happy about a more detailled response:

String backgrounds determine a CFT, in this CFT there is a state-operator correspondence and the vertex operators used in string scattering computations are given by this correspondence in terms of the external scattering states one is interested in. This is discussed in Chapters 2,3 of volume I of Polchinski's book on string theory.

answered Jun 11, 2013 by Dilaton (6,240 points) [ revision history ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysic$\varnothing$Overflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...