A QHE ' the effective action should be a local functional'

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' Finally, if we care only about long distances, the effective action should be a local functional, meaning that we can write is as ##S_{eff}[A]=\int d^d x...## '

Where does this come from and what does it mean? This isn't at all familiar with me, and I don't recall ever seeing anything similar. Thanks.



http://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf , page 145 David Tong notes QHE , chapter 5
 
Last edited:
1,182
8
' Finally, if we care only about long distances, the effective action should be a local functional, meaning that we can write is as ##S_{eff}[A]=\int d^d x...## '

Where does this come from and what does it mean? This isn't at all familiar with me, and I don't recall ever seeing anything similar. Thanks.



http://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf , page 145 David Tong notes QHE , chapter 5
Also in his notes I see he uses ##A \to A + \partial_{\mu}## as a pose to ##D_{\mu} \omega ##, is this linked to the above? Is this sort of anagolous to GR where the 'connection vansihes' in this approximation or something - I make out the terms connection and potential are related from the notes but must differ somehow- in particular he later refers to ##a_{\mu}## as a connection as a pose to a potential (on the discussion of non-Albelian CS), the covaraint derivaitve I believe is defined to be the partial \pm i connection/potential ..I'm not sure exactly which formally, thanks
 

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