# What gives an elementary particle a charge? [duplicate]

We know that proton is positive, and electron is negative. But where does come notion of negativity and positivity? Does charge come from some specific particles, or they specific order?

• Can you help me understand the question a bit better? If you are asking "What is charge?" then I point out that this question has been asked and answered here several times. Look here for some answers and links to others, or use the search box in the upper left corner of the page. Or help me understand the question. – garyp Jul 6 '14 at 12:37
• @garyp, sure, thanks for you attention btw, this question should be better stated as "what does give an elementary particle a charge". – PaulD Jul 6 '14 at 12:39
• Ok, then please edit your question to clarify what you mean. And I'll point you to this post, and again refer you to the search box. If you have further specific questions, start a new question. – garyp Jul 6 '14 at 12:43
• possible duplicate of Is there any theory for origination of charge? – garyp Jul 6 '14 at 12:47
• While the question is not at all the same, it is worth reading this answer by Mark Eichenlaub; at the deepest heart, physics is a descriptive discipline and somewhere, down at the very bottom of the "Why?"s is the answer "That's just the way it is". Every time. – dmckee --- ex-moderator kitten Jul 6 '14 at 14:09

## 1 Answer

There are various layers one could address your question.

As all observables in QM, the charge exist because there exist a self-adjoint operator associated to it. This operator corresponds to a (class of) experimental instruments that the observers use to make measurements on the system, the collection of possible numerical outcomes being known as charges.

Another answer, perhas deeper, could be that the existance of such an operator $Q$ (an thus the associated instrument) is guaranteed, as for most of the relevant operators in QM, by the Noether theorem associated with a $U(1)$ global symmetry of the action. We can thus say that the charge exists because there the dynamics is invariant under a certain $U(1)$ symmetry group. Moreover, we know that $[Q,H]=0$ and therefore the electric charges is also conserved in time.

There are other layers. One is specific to the electric charge: it is not only corserved, it is also superselected i.e. it commutes with all physical observables. This means that any physical state is always in a definite charge state. It is not possible to prepare a system with non-definite electric charge (as it is instead possible, for example, with the spin for which one can take linear cominations of states up and down). In particular, any one-particle state will have definite electric charge.

Finally, since the charge is exactly conserved, any composite system made of more elementary stuff (say the proton is made of quarks and gluons), will have exactly the same charge that the sum of its elementary constituents. In other words, a system of ''free'' constituents and the bound constituents have the same net electric charge. For a proton we can say that the electric charge +1 comes from the fact that the up-quarks carry charge 2/3 and the down quarks -1/3. Their electric charge is fixed, up to overall normalization, by the anomaly cancellation in the SM which can be naturally explained in GUT theories (including in this case the normalization if the larger group is simple).