# Every known boson and fermion has a corresponding anti-particle

Please take a moment to help enlighten a poor ignorant layperson. My understanding is that every known boson and fermion has a corresponding anti-particle, with the only exception being the photon. If true, can anyone explain WHY that that is?

fzero
Homework Helper
Gold Member

The photon is not an exception, it is its own antiparticle. Certain electrically neutral particles are also their own antiparticle, including the Z-boson and neutral pion.

Drakkith
Staff Emeritus

The photon is not an exception, it is its own antiparticle. Certain electrically neutral particles are also their own antiparticle, including the Z-boson and neutral pion.

Got a link to something that explains this Fzero? Curious myself.

fzero
Homework Helper
Gold Member

Got a link to something that explains this Fzero? Curious myself.

If we're just talking about the photon, there's a nice demonstration in Ch 10 of Weinberg V1. There he shows that the electric current transforms under charge conjugation as

$$C: \bar{\psi}\gamma^\mu \psi \rightarrow - \bar{\psi}\gamma^\mu \psi.$$

You can work this out explicitly knowing how the Dirac spinor transforms under $$C$$. Now, if we want $$C$$ to be a symmetric of QED (and it's known to be a symmetry of the classical theory), then the photon must transform as

$$C: A_\mu \rightarrow - A_\mu$$

in order that the interaction term be invariant. Therefore the photon is its own antiparticle.

One could have already seen this from second-quantization, by noting that there's only one type of creation operator in the field expansion.

Things get more complicated if we're dealing with electrically neutral particles that have other types of charge. In particular, the neutral kaon has strangeness charge 1, so it cannot be it's own antiparticle. Instead there are mixed states of $$K^0$$ and $$\bar{K}^0$$ that are each their own antiparticle. The discussion on wikipedia is decent, but any particle physics text (such as Griffiths) would discuss this.

Drakkith
Staff Emeritus

Heh, thanks Fzero. I have almost no idea what any of that means but thats ok. I'm not exactly studied up on that kind of math and such. =)

Charge conjugation, particle <-> antiparticle, reverses electric charge. To be consistent, the electromagnetic field must reverse sign. But aside from that, it stays the same as before.

Elementary fermions have antiparticles that are distinct from them. Their main bound states are mesons (quark-antiquark) and baryons (quark-quark-quark). Baryons have separate antibaryons, but mesons can be their own antiparticles. They will be that if they are flavor-neutral: flavor-antiflavor.

A neutral pion is ((up,antiup) - (down,antidown))/sqrt(2)
a mixed state

An eta meson is a mixture of ((up,antiup) + (down,antidown))/sqrt(2) and (strange,antistrange)

A J/psi meson is (charm,anticharm)

An upsilon meson is (bottom,antibottom)

Etc.

The photon is not an exception, it is its own antiparticle. Certain electrically neutral particles are also their own antiparticle, including the Z-boson and neutral pion.

There was a time a group of physicists found evidence pointing to the existance of antiphotons in their experiment. They refuted it to the point of calling it nonsense... http://www.economist.com/node/13226725?story_id=13226725 we have never found the existence of a fermionic majorana particle however.