- #1
Ahmes
- 78
- 1
Hello,
I took an Electrodynamics course this semester, where we derived Maxwell's equations from the field's Lagrangian density.
As a motivation, we "looked" for a scalar (in the relativistic sense) having something to do with EM fields - and had we found one we would have declared it a candidate to be our Lagrangian density.
We found two such scalars (in the characteristic polynomial of the EM tensor): [itex]|\mathbf{B}|^2-|\mathbf{E}|^2[/itex] and [itex]\mathbf{E}\cdot\mathbf{B}[/itex]
The professor hand-wavingly claimed that the latter "does not preserve parity" and therefore invalid, so we ignored it for the rest of the course. But now (after the test...) I came back to this dot product, trying to see what "new Maxwell equations" we can theoretically get from it.
I wrote it using the 4-vector-potential and its derivatives, put it in the Euler Lagrange equations - and surprisingly - this element contributes nothing! Putting it in the EL equation just produces zero.
So what is the story of the parity and how does it relate to E dot B?
I took an Electrodynamics course this semester, where we derived Maxwell's equations from the field's Lagrangian density.
As a motivation, we "looked" for a scalar (in the relativistic sense) having something to do with EM fields - and had we found one we would have declared it a candidate to be our Lagrangian density.
We found two such scalars (in the characteristic polynomial of the EM tensor): [itex]|\mathbf{B}|^2-|\mathbf{E}|^2[/itex] and [itex]\mathbf{E}\cdot\mathbf{B}[/itex]
The professor hand-wavingly claimed that the latter "does not preserve parity" and therefore invalid, so we ignored it for the rest of the course. But now (after the test...) I came back to this dot product, trying to see what "new Maxwell equations" we can theoretically get from it.
I wrote it using the 4-vector-potential and its derivatives, put it in the Euler Lagrange equations - and surprisingly - this element contributes nothing! Putting it in the EL equation just produces zero.
So what is the story of the parity and how does it relate to E dot B?
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