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binbagsss
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Homework Statement
Part C) Please:
Homework Equations
above,below
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):
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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