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Old Dec 28th 2017, 09:08 AM   #1
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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.
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QFT T-duality, Massless vector states-pf2-1-.png   QFT T-duality, Massless vector states-pf2-2-.png  
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Old Apr 28th 2018, 05:37 PM   #2
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How can the gauge to used to represent a particle structure ? since an expanding field structure, well expands!
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Old Apr 28th 2018, 08:30 PM   #3
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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
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Old Apr 28th 2018, 08:36 PM   #4
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Originally Posted by lovebunny View Post
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
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Old May 18th 2018, 01:04 PM   #5
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Originally Posted by topsquark View Post
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
Many thanks for your reply.
I'm using lecture notes from my uni.
I find David Tong's lecture notes on String Theory useful too-just google it wil come up.
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