About the derivation of Lorentz gauge condition

  • #1
The question:
Show that the Lorentz condition ∂µAµ =0 is expressed as d∗ A =0.
Where A is the four-potential and * is the Hodge star, d is the exterior differentiation.


In four-dimensional space, we know that the Hodge star of one-forms are the followings.
0c95a67c2cdabbfc965b8475ec01a96f4bce3af9


3. My attempt
Since the four potential one-form is
png.png

Therefore we have
png.png

Then d*A = 0 is equivalent of saying
png.png
(Where
png.png
)

However, the actual Lorentz gauge potential is
png.png
(Where
png.png
)

I don't know why there is a sign difference?
 

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Answers and Replies

  • #3
Aren't the indices "upstairs", here?
Opps, such a silly mistake........ thank you!
 
  • #4
dextercioby
Science Advisor
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The correct name is Lorenz, not Lorentz. Please, tell that to your instructor, too.
 

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