Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

What does it mean for a field (say, $\phi$) to have a charge (say, $Q$) under the action of a group (say, $U(1)$)?

share|cite|improve this question
up vote 5 down vote accepted

It means that

  1. the charge operator $Q$ is a Lie algebra generator for some Lie group $G$.

  2. the field $\phi\in V$ takes values/transform in a representation $V$ of the Lie group. (Note that any Lie group representation $V$ is also Lie algebra representation of the corresponding Lie algebra.)

  3. the charge operator $\rho(Q)$ in the representation $\rho: G \to GL(V)$ is proportional to the identity. The proportionality factor/eigenvalue is the actual charge of the field.

To see an example of this, say the (strong) $u(1)$ hypercharge $Y$, see this answer.

share|cite|improve this answer
Thank you, it helped a lot! – John Smith Mar 2 '12 at 16:05

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.