# What parity has an electron?

I couldn't find anything about the parity of an electron. Neither in the german, nor in the spanish and nor in the english version of Wikipedia.

I only found one sentence in the parity article of Wiki:

One way to fix a standard parity operator is to assign the parities of three particles with linearly independent charges B, L and Q. In general one assigns the parity of the most common massive particles, the proton, the neutron and the electron, to be +1. - Wiki

But I cannot find other sources to confirm it.

I do not need it for a special exercise, it's just to understand the whole thing...

## 2 Answers

spin 1/2 fermions (electron, proton, neutron, muon, tau, quarks) have +1 parity (by convention as pointed out in Anna's comment). The corresponding anti-fermions have -1 parity.

Bosons and their anti-particles have the same parity.

See this and this lecture for more information on parity.

• maybe one should note that it is a convention, to give +1 to particles and -1 to their antiparticles. By this convention it was determined that parity is conserved in strong interactions. Mar 27, 2014 at 20:19
• @annav I thought that electron, proton, neutron having +1 parity is the convention. Then the positron, antiproton, antineutron having -1 parity is required, and not a convention. Mar 27, 2014 at 20:40
• @anna that's only true for fermions. Mar 27, 2014 at 21:12
• @innisfree right, the parity of bosons can be measured once one has a system . My comment was with respect to the original answer which was correct but not complete. Mar 28, 2014 at 4:10
• These lectures are not really correct. There exist the intrinsic parity (IP) of a particle, which is what QFT deals normally with, and there is the parity of the particle's wavefunction (WF), which is normally used in atomic or nuclear physics (QFT rarely). The author mixes them up. The IP of a photon is -1. The IP of an electron is +1. Period. On the other hand, the WF parities of a free photon and of a free electron are not not defined since those WFs are just plane waves (PWs), and PWs don't have defined parity. You may expand PWs in multipoles. Then each multipole has different parity. Nov 11, 2016 at 22:03

Intrinsic parity is determined by experiments , but it is impossible to determine it for the electron or other leptons . But conventionally, it is said that it is for the $e$, $\tau$ and $\mu$, $P = 1$ (according to the book of Martin and Show of particle physics, 3rd edition, chapter 5, section 3, page 130)

$$P(e) = P(t) = P(u) = 1$$ and $$P(\text{anti}\ e) = P(\text{anti}\ \tau) = P(\text{anti}\ \mu) = -1$$

• Why is it impossible to determine it experimentally (for leptons) ? Mar 6, 2017 at 18:59
• Because leptonic number L is conserved in all interaction . So , in calculations, the parity of an electron cancels out in both sides (the initial and final states of an interaction) and we are left with no clue ! Mar 6, 2017 at 19:16