Re: Electric / Magnetic Duality

On Apr 10, 11:15 am, "Jay R. Yablon" <jyablon@xxxxxxxxxxxx> wrote:

The upshot of the derivation at
http://home.nycap.rr.com/jry/Papers/Dirac%20Quantization.pdf
is that the (unique up to a gauge transformation) solution to the
differential equation *(dA)= (dM), is:

g_e A = g_m M (1)

This cannot possibly be true for all A. Take for instance, A = y dx.

Also, note that even if your solution were correct, it would completely
wipe out any difference between electric and magnetic charges. There
will be only one current coupling to A.

How would one go about determining whether the solution (1) is or is not
non-local?

Not a single solution. A linear (single valued) mapping that associates
to A a solution M of *(dA) = dM will be non-local. It will involve
integration against some sort of non-trivial Green function, M(x) = int
G(x,y) A(y). Unless G(x,y) is a linear combination of finitely many
delta functions and derivatives of delta functions, the expression for
M(x) will be non-local (by definition).

Let's take this first, then, if we can clear this issue, we can discuss
the zero kinetic term.

This is a case of putting the cart before the horse.

Igor

.

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