Making electrons covariant

1. Jul 24, 2004

kurious

What is meant by " if an electron has size it would be difficult to be make covariant" in quantum field theory.Does this mean the electron would
behave differently in different frames of reference,or does it just mean that the electron would not be in a state that allows it to fit into the mathematical
framework of QFT which I assume involves tensor analysis.And could an
electron ,that has size, be broken down into a series of points and each point be made "covariant" , and then all the covariant results be added
together to represent the electron overall?

2. Jul 24, 2004

marlon

Normally covariant means the equations are the same in any frame of reference, so indeed covariant electrons behave in the exact same way in each frame. I don't really know what you mean by size, but could it be that you mean mass??

Because an electron in QFT cannot have mass before the spontanous breakdown of symmetry. The reason for this is that mass mixes the left and right-hand sized chirality component of the elektron wave function. It is so that these two components are fundamentally different so any elementary particle must have mass zero in order to be convariant (in order to behave in the same way in every frame).

Mass is generated by the Higgs-mechanism.

3. Jul 24, 2004

Tom Mattson

Staff Emeritus
Maybe he's talking about Dirac spinors?

4. Jul 24, 2004

marlon

Possible, but when you are talking about spinors, you are really talking about the elektronspin, right ???

In this case i don't see no pronblems concerning covariance, because the transformation-properties of the spinorrepresentation are well known. Turn 360° and we get the opposite spin, turn another 360° and we get the spinorientation from which we started.

I don't know, just a thougt...

5. Jul 25, 2004

kurious

I meant that an electron isn't a point-like particle when I said "size".
QFT can't be done if an electron isn't point-like.Is that correct?
And I think it can't be done because of this problem with making the theory covariant when an electron isn't point-like.Dirac didn't think QFT was a good theory becuase he didn't think the correct field theory for electricity would give rise to infinities that have to be renormalized.If an electron isn't point-like
and a field theory for electricity was based on this idea, then theorists seem to think that the electron must be made covariant.But what if it doesn't have to be covariant?

Last edited: Jul 25, 2004
6. Jul 25, 2004

marlon

In QFT the elementary particles must be pointlike with no internal structure. The reason for this is that if they were to have a dimension, they would undergo a Lorentz-Fitzgeral-Contraction because we always need to have a finit propagation-speed between different reference frames. So particles with dimension would be deformed due to tidal-force-effects. This cannot be the case as explained by experiments.

I don't get what you mean by Dirac his dislike for the fieldtheory for electricity. It is so that he had a problem with the fact that Maxwellequations did not contain perfect symmetry between electricity and magnetism. There is no "brother" for electric charges. That is why he introduced the concept of magnetic monopoles back in 1948. It is so that these monopoles have yet to be seen in experiments, though they do exist in there as an antisymmetric tensorfield, called the Dirac-string. These things are used in the creation of a lineair potential in order to explain the quarkconfinement.

Also pay attention to the fact that in field-theories alla yang-Mills, the electronwavefuntion is always covariant. it is this model that predicts the fotonfield as a bosonic field which is to be viewed as the force-carrie field. the reason why force carries have integer spin comes from the second-quantization-procedure. They had to be indistiguishable in order to respect the canonical commutationrelations of the second-quantization. if these rules are not respected fotons would have un-phisical-properties like negative-probability-amplitude. They would become things like ghosts from a fadeev-Popov-determinant.

greetz
nikolaas van der heyden

7. Jul 25, 2004

kurious

Marlon:
particles with dimension would be deformed due to tidal-force-effects

Kurious:

How do we know that Lorentz-Fitzgerald contraction occurs at very small distance scales?
Has anyone ever considered the idea that length contraction in special relativity could be quantized and that the radius of a particle could stay constant for observers over a wide range of velocities?

Last edited: Jul 25, 2004