# Can a massless particle have both spin and charge?

Can a hypothetical elementary particle, at least in theory (according to the current science), have 0 mass and yet also have both spin and electrical charge (at the same time)?

• I imagine you're talking about electric charge but gluons are spin-1 particles with colour charge. – Charlie Oct 21 '20 at 22:22
• To be sure, the (electrically) charged weak vector bosons are massive because the vacuum is an electroweak superconductor, i.e., they're zero mass, charged particles before the non-zero Higgs VEV hides the symmetry. Would this qualify for your "hypothetical elementary particle" or are you looking for something else? – Alfred Centauri Oct 21 '20 at 22:23
• @Charlie i should prolly clarify that – Chao Somnium Oct 21 '20 at 22:24
• @AlfredCentauri that's not what i'm looking for – Chao Somnium Oct 21 '20 at 22:25
• Possible duplicates: Massless charged particles and links therein. – Qmechanic Oct 22 '20 at 5:43

Can a massless particle have both spin and charge?

Spin is the value assigned to measured elementary particles , including photons which are massless . Photons need to have spin 1 in order to have conservation of angular momentum in the electromagnetic interactions.

Charge also is a measured quantum number assigned to elementary particles and by conservation to their composites. Photons have zero charge, by observation.

The quantum field theoretical standard model is chosen because it fits the data and in its representations there are no states with 0 spin, massless, that have electric charges, by construction . The model is chosen to fit the data.

So, if we had observed a zero mass particle with electric charge, we would have found a different theoretical model as a standard one, in order to fit the data. As mentioned in the comments to the other answer, the gluons are zero mass, spin one , and are assigned a colored charge in the SM in order for the model to fit the data.

The answer to your question is that at the present level of observations there are no massless electrically charged particles observed and the theory has been chosen to fit the data, so the theory does not allow for a massless particle with spin to be electrically charged.

• Dear Anna. You have given a lot of answers on various questions that are basically "The data says so, theory is made to fit the data, if the data were different then theoreticians would work it out". These answers really lack substance and don't take into account that some differences would mean trivial changes to the theory while other would require something radical. – OON Oct 22 '20 at 22:10
• Besides, this statement "so the theory does not allow for a massless particle with spin to be electrically charged" puts your answer on its head and is wrong. The qft model with charged massless spinors can be consistent (as long as gauge anomalies cancel out). So theory ALLOWS them. It would no longer fit the data but that's not theory, rather its predictions confronted with experiment. – OON Oct 22 '20 at 22:26
• @oon By "theory" I m refering to the specific standard model of particle physics. Of course one can make a QFT for anything. The specific fitted model does not allow it. – anna v Oct 23 '20 at 4:25
• Yes , in my opinion a physicist, either of theoretical or experimental inclination, is not a mathematician. Physicists observe nature; the experiments record it, the theory models it. Sure with new data some extensions of theoretical models tofit it are easy, some are not. For me this is the basic substance, that observation of nature comes first , There is the platonic view, essentially that mathematics creates reality to which a lot of people are implicitly followers, but until a "a theory of everything" is found , this is – anna v Oct 23 '20 at 4:36
• an open question en.wikipedia.org/wiki/Platonic_idealism "Plato's idealism evolved from Pythagorean philosophy, which held that mathematical formulas and proofs accurately describe the essential nature of all things," – anna v Oct 23 '20 at 4:36

In the standard model, every massless particle transforms under representation of $$U(1)_{EM}$$ group. Therefore, every particle has an electric charge (some of them transform in the trivial representation and therefore have zero electric charge). On the other hand, spin is not well defined for a massless particle, since it's a quantity natural to the rest frame of the particle. Instead massless particles carry helicities, which are analogous to spin, although the word spin continues to be used colloquially. This is because massive particles transform in representations of their little group $$SO(3)$$ a.k.a spin, but massless particles transform in representations of $$SO(2)$$ a.k.a helicity.

So, to answer your question: massless particles carry can charge but not spin (in the strictest sense of the word).

A gentler, a less jargon filled explanation would be as follows: Technically there is nothing prohibiting a massless particle from carrying charge. The intuitive notion of a massless particle being affected by radiation continues to hold in the standard model. On the other hand, spin is subtler in that it requires you to think about what exactly is spin. One way to think about spin is to apply a magnetic field to the particle in its rest frame and ask how many possible configurations the particle has. However, for massless particles, relativity prohibits you from catching upto the particle and thinking of a rest frame for the particle. For massless particles the notion of spin is replaced by helicity.

• With reference to the lack of rest frame for a massless particle, does that mean a charged massless particle would still move at c? If so, does GR have anything to say about the possibility (or behaviour) of such a particle? – Penguino Oct 21 '20 at 23:32
• Yes, it would move at the speed of light. I am not sure the second question is concrete enough to write down a definitive answer. I will say that universality of gravitational interaction constrain this particle to have a helicity less than $\frac{3}{2}$. – Anonjohn Oct 21 '20 at 23:35
• every particle has an electric charge is not true. You mean every massive particel of the standard model? Even that is wrong since the higgs boson is neutral (and spin zero) – mary_stein Oct 22 '20 at 4:19
• Please read what I have said. Electric charge is the eigenvalue of the one particle state under an operator, and some of them have- zero eigenvalue. The ones with zero Eigen value dont couple to the photon and are "uncharged". Those that have a non zero eigenvalue do. At no point did I say all particles have non zero charge. What I am saying is almost a tautology, but meant to clarify that all particles could potentially be charged. – Anonjohn Oct 22 '20 at 4:36
• People who have experience in QFT understood but many that are learning do not. I agree with @mary_stein and think you should probably clarify this point in your answer. – Dr jh Oct 22 '20 at 4:48