3 dimensional gauge theory

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Dear all
I have a question is the dual of the field strength ( of abelian gauge theory) in 3 dimensional space the same as the gauge field?
I have a formula for the dual field strength and am trying to bring that of gauge field!!!
Thank you
 

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Orodruin
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Do you mean in 1+3-dimensional or 1+2-dimensional space time?

In the first case, the dual is also a 2-form, but generally not the same 2-form. In the second case, the dual is a 1-form, not a 2-form. (In an N dimensional space the dual form of the field strength is N-2-dimensional.)
 
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  • #3
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Do you mean in 1+3-dimensional or 1+2-dimensional space time?

In the first case, the dual is also a 2-form, but generally not the same 2-form. In the second case, the dual is a 1-form, not a 2-form. (In an N dimensional space the dual form of the field strength is N-2-dimensional.)
Hi again
no i mean in 1+2 space yes i know that the dual of a k vector is N-k. But am applying it to N= 2+1 space, i am wondering if the dual of the field strength which is a 1 form is the same as the gauge field since both are 1 form in this special 1+2 space.
Thank you again
 
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Orodruin
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The field strength is given by ##F = dA## and since ##A## is a one-form, ##F## is a 2-form. Are you thinking of the gauge potential ##A## when you say gauge field? The answer is still no, the dual of ##F## contains derivatives of ##A## and ##A## does not, you would be saying ##*dA = A##.
 
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