# Electron chirality

1. Oct 29, 2015

### kimcj

(1) electron = left chiral . anti electron = right chiral. positron = left chiral. anti positron = right chiral. So scalar couples L and R chiral fermion fields.
(2)electron = left chiral . anti electron = right chiral. positron = right chiral. anti positron = left chiral. So scalar conserves chirality.

Im pretty sure 1 is right. However in flip tanedos article he says that the anti positron has left chirality........

Is 1 right??

Im definate that (1) is right. However in flip tanedos 'feynman diagrams for undergrads- helicity chirality and the mass' has some confusing phrases saying that the anti positron is left chiral.....

Is (1) right??

2. Oct 29, 2015

### Staff: Mentor

3. Oct 29, 2015

### Staff: Mentor

A positron and an anti-electron are the same thing. So are an anti-positron and an electron. So (1) doesn't even make sense; it contradicts itself.

4. Oct 30, 2015

### kimcj

No i dont mean the physical mass based electrons and positrons. i mean the spinor componets of the electron and positron

5. Oct 30, 2015

### Staff: Mentor

In other words, you are referring to a 4-component Dirac spinor, and you are calling the upper two components the "electron" and "anti-electron", and the lower two components the "positron" and "anti-positron"? That's not correct terminology, and that may be why you are getting apparently different answers from the article you read (do you have a link?).

If you want to view a 4-component Dirac spinor as being "made of" two 2-component Weyl spinors, then the first 2-component spinor would be the "electron" and the second 2-component spinor would be the "positron". It is still true, as I said, that "positron" and "anti-electron" are the same thing, and "anti-positron" and "electron" are the same thing.

The chirality of the components themselves depends on which basis you choose. In the Weyl basis, each 2-component Weyl spinor has definite chirality for both components--the first component is left and the second is right. In the Dirac basis, however, that is not the case. In the Weyl basis, the first 2-component spinor would have components called "left-handed electron" and "right-handed electron", and the second would have components called "left-handed positron" and "right-handed positron".

As far as making scalars out of these spinors, the mass term $\bar{\psi} m \psi$ couples terms of left and right chirality, and the kinetic term $\bar{\psi} \gamma^{\mu} \partial_{\mu} \psi$ couples terms of the same chirality (left and right separately).

6. Oct 30, 2015

### Staff: Mentor

By the "Flip Tanedo" article, do you mean this?

7. Oct 30, 2015

### vanhees71

Just to clarify this, an electron is of course not the same as a positron. The electron is negatively and the positron is positively charged. They are particle and antiparticle, described by massive Dirac (bispinor) field. They are thus not of definite chirality but consist of both left- and right-handed spinor components, as already is clear from the mass term $\bar{\psi} \psi=\bar{\psi}_L \psi_R + \bar{\psi}_R \psi_L$.

For details, have a look at the first theory lecture here:

http://fias.uni-frankfurt.de/~hees/hqm-lectweek14/index.html

8. Oct 31, 2015

yes....