Parity in Electromagnetism

[decraig]

In the normal description, E, J and the vector potential A are taken to be vectors. B is an axial vector. q is a scalar.

 

Would any physical description change should these roles be reversed?

 

For example, B would become a vector, E would become an axial vector, and q a pseudo scalar.

 

 

[ajb]

Are you asking about S-duality?

 

http://en.wikipedia.org/wiki/S-duality

[decraig]

No, not the E-B vacuum duality, though interesting in itself and may be extended using complex charge. It's the same as the F-G duality, where F is the Farday tensor and G its Hodge dual. It's extended using F+iG --> *(iF-G), and **(iF-G)--> -F-iG, if I recall. * is the Hodge duality operator. The magnetic charge can removed with a global gauge change.

 

I'm asking about PT symmetry in Maxwell + Lorentz force.

Edited January 12, 2014 by decraig

[studiot]

q as a psuedo scalar?

 

How would that work?

 

http://en.wikipedia.org/wiki/Pseudoscalar

[decraig]

q as a psuedo scalar?

 

How would that work?

 

http://en.wikipedia.org/wiki/Pseudoscalar

In short, charge would change sign upon conjugating any spatial coordinate. e.g.: [math]C(x^i)=-x^i[/math]

 

In the usual div-grad-curl calculus used, the declaration doesn't derive from anywhere--its just declared.

 

But we can do a little better, as follows.

 

In preliminarty justification, total charge, Q is the integral over a space-like region of charge density, q = q(x,y,z). [math]Q= \int _s q[/math].

q is the charge density, a type (0,3) tensor. It may appear as if the integrating infinitesimals are missing. They are not; but are the tensor bases. If the volume element is oriented we could define charge density as q = q_{xyz} dxdydz where q is antisymmetric in all indices. The sign of Q follows the sign of q.

Edited January 12, 2014 by decraig

[decraig]

This, however, should still be do-able in the usual calculus, Studiot

[studiot]

That does not answer this statement extracted from my link.

 

 

However, under the parity transformation, pseudoscalars flip their signs while scalars do not. As reflections through a plane are the combination of a rotation with the parity transformation, pseudoscalars also change signs under reflections.

 

As I understand it this would require charge to change sign under transformation from a left handed coordinate system to a right handed one, something we know does not happen.

[decraig]

That does not answer this statement extracted from my link.

 

 

As I understand it this would require charge to change sign under transformation from a left handed coordinate system to a right handed one, something we know does not happen.

No, I mean doable as in solvable.

 

If the assigned charges in your measuring instrument also changed sign, there would be no measurable effect. But I see what you mean. For a local parity change on a system, where the observer is outside a region of coordinate invertion--which is what you are talking about--there would be a measurabe difference. But what of a global change?

Edited January 17, 2014 by decraig

[acsinuk]

The fundamental question you pose is are there rear and imaginary components in Electromagnetic light. Well Faraday discovered electromagnetism and electrical energy long ago and later established that light was electromagnetic also. A really knowledgable article on Faraday effect on rotation in Wikipedia states in its final paragraph
"The composite magnetic/plasmonic nanostructure can be visualized to be a magnetic particle embedded in a resonant optical cavity. Because of the large density of photon states in the cavity, the interaction between the electromagnetic field of the light and the electronic transitions of the magnetic material is enhanced, resulting in a larger difference between the velocities of the right- and left-hand circularized polarization, therefore an enhanced Faraday rotation."

The power grid runs at only 50 hertz but still the current moves at nearly the speed of light. AC electric theory is easier to study than light and engineers are well aware that grid power is comprised of an area of current being pulled forward by a voltage at right angles to the current. If the phase angle is incorrect then the 3D electric power is reduced by the cosine of the angle and reactive current [ either inductive or capacitive] produces VAR's which are imaginary power instead of Watts.

I am not aware that any physicists have yet identified the rear and imaginary components of a light or whether the 2 3D components will rotate in opposite directions as expected in the Euler series.
CliveS

[swansont]

What is a "rear" component of an EM wave? At the first instance I assumed this was a typo for "real" but you used it twice.

 

What does Faraday rotation have to do with the discussion?

[acsinuk]

Sorry for the typo. Yes, I mean the real and imaginary components of EM light. The parity connection is from the idea that the real EM component helixes forward clockwise but imaginary EM component helixes forward anticlockwise. This is mathematically similar to the Eular progression as during any 2 cycles together both average to zero but yet exists as an electro-magnetic tube or tunnel through which the 3D electricity or light passes. Thus, external electric or magnetic fields do not affect the overall velocity or angle of transmission.

CliveS