# What is charge? i do not want to hear that it is of two kind

1. Mar 11, 2012

### nouveau_riche

what is charge?
i do not want to hear that it is of two kind :positive and negative
i just want to know if there is a fundamental definition of charge like mass?

2. Mar 11, 2012

### conquest

Re: charge

Hi nouvea_riche,

Charge is a fundamental property of things. What fundamental definition of mass do you mean? That might make it easier to formulate an answer in the same way.

3. Mar 12, 2012

### tom.stoer

Re: charge

It's a bit complicated.

If you look at Maxwells's theory you see the 'e' in the equation. This is not really a charge but a coupling constant. The charge Q is defined in terms of the charge density ρ and is conserved due to Noether's theorem.

$$Q = e\int_{\mathbb{R}^3}d^3x\,\rho(x)$$

$$\frac{dQ}{dt} = 0$$

In QED the charge is no longer arbitrary but can be defined in terms of the electron and positron field ψ. There are now operators ρ and Q:

$$\rho = j^0 = \psi^\dagger \psi$$

Again Q is defined as an integral and is conserved, i.e.

$$[H,Q] = 0$$

The proof in QED goes beyond Noether's theorem b/c we have to deal with (renormalized) operators instead of classical fields.

What we observe in nature are states (electrons, positrons, ...) which are eigenstates of Q, i.e.

$$Q|\psi\rangle = q|\psi\rangle = ne|\psi\rangle$$

with n=0,±1,±2,...

Afaik there is no proof in standard QED that the eigenvalues q of Q are always quantized in integer units of e, i.e. that q=ne must always hold. In addition afaik there is no proof that physical states are always eigenstates of Q, i.e. that something like

$$|\psi\rangle = |n=1\rangle + |n=2\rangle;\;\;Q|n\rangle = n|n\rangle$$

must not exist.

Last edited: Mar 12, 2012
4. Mar 12, 2012

### PhilDSP

Re: charge

James Clerk Maxwell defined charge as a discontinuity of polarization. He apparently drew that idea from Clausius Mossotti who earlier built a theory of electricity based on how a medium can be polarized.

5. Mar 13, 2012

### tom.stoer

Re: charge

there are some reasons (especially in non-abelian gauge theories) that total charge is always zero for physical states, i.e. Q|phys> = 0, but this is not completely rigorous; note: in QCD is color-neutrality is different from color-confinement!

6. Mar 13, 2012

### nouveau_riche

Re: charge

like resistance to acceleration for mass

7. Mar 13, 2012

### nouveau_riche

Re: charge

all maths,i need theoretical

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