Physics Help Forum QFT T-duality, Massless vector states

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 Dec 28th 2017, 09:08 AM #1 Junior Member   Join Date: Nov 2017 Posts: 3 QFT T-duality, Massless vector states 1. The problem statement, all variables and given/known data Part C) Please: (attachment 1) 2. Relevant equations above,below 3. The attempt at a solution so I think I understand the background of these expressions well enough, very briefly, changing the manifold from $R^n$ to a cylindrical one- $R^{(n-1)}^{+1}$ we need to cater for winding modes, the momentum and winding momentum for the circular dimension can not take arbitrary values and are quantified, $n,m \in Z$ And importantly, the level-matching constraint is no longer required to hold and instead replaced by the second equation in c) . For the combinations I get: a) $n=m=0$ $N=\bar{N}=1$ b) $n=m=1=N$ $\bar{N}=0$ c) $n=2$ $m=0=N=\bar{N}$ d) $m=2$ $n=N=\bar{N}=0$ I am completely stuck on which of these combinations transforms as a vector. The only notes relevant to it I seem to have is the following attached, (bit underlined in pink): (attachment 2) Is this referring to the ladder operator carrying a transverse index? or the state |p> ? So out of the combinations above I have: a) would require both a $\alpha^j$ and a $\bar{\alpha^j}$ b) would require just a $\alpha^j$ c) & d) would require no ladder operators. Is the above relevant/needed at all or not, for what transforms as a vector or what doesn't, what defintion am I needing to go by here? Many thanks in advance. Attached Thumbnails
 Apr 28th 2018, 05:37 PM #2 Banned   Join Date: Apr 2018 Posts: 92 How can the gauge to used to represent a particle structure ? since an expanding field structure, well expands!
 Apr 28th 2018, 08:30 PM #3 Forum Admin     Join Date: Apr 2008 Location: On the dance floor, baby! Posts: 2,454 Hey binbagsss if you still happen to be around I am trying to teach this stuff to myself without benefit of someone to ask questions of. Can you tell me what text you are using and if you think it's a good text to work from? Thanks. -Dan __________________ Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup. See the forum rules here.
Apr 28th 2018, 08:36 PM   #4

Join Date: Apr 2008
Location: On the dance floor, baby!
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 Originally Posted by lovebunny How can the gauge to used to represent a particle structure ? since an expanding field structure, well expands!
This looks like a good page.

The first response is a good intro to the topic. The first link in the second response looks like it could be good fun(!) but I didn't actually fire it up and take a good look.

-Dan
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

May 18th 2018, 01:04 PM   #5
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Join Date: Nov 2017
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 Originally Posted by topsquark This looks like a good page. The first response is a good intro to the topic. The first link in the second response looks like it could be good fun(!) but I didn't actually fire it up and take a good look. -Dan