# A 3 dimensional gauge theory

1. Sep 30, 2016

### shereen1

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

2. Sep 30, 2016

### Orodruin

Staff Emeritus
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.)

3. Sep 30, 2016

### shereen1

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

4. Sep 30, 2016

### Orodruin

Staff Emeritus
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 $*dA = A$.