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

• nouveau_riche
In summary: Charge is a fundamental property of things that is defined in terms of the charge density and is conserved. In QED, the charge is no longer arbitrary and can be defined in terms of the electron and positron field. There are now operators ρ and Q: Q=e\int_{\mathbb{R}^3}d^3x\,\rho(x) and \frac{dQ}{dt}=0. In terms of states, we observe that things are eigenstates of Q if and only if Q|\psi\rangle=q|\psi\rangle=ne|\psi\rangle. There is no proof
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?

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.

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:

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.

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!

conquest said:
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.

like resistance to acceleration for mass

tom.stoer said:
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.

all maths,i need theoretical

## What is charge?

Charge refers to a fundamental property of matter that causes it to experience electromagnetic interactions. It is a measure of the amount of electric energy in an object.

## How is charge measured?

Charge is measured in units of Coulombs (C). One Coulomb is equivalent to the amount of charge that passes through a conductor in one second with a constant current of one ampere.

## What are the two types of charge?

The two types of charge are positive and negative. Positive charge is associated with protons and negative charge is associated with electrons.

## Can charge be created or destroyed?

No, charge cannot be created or destroyed. It can only be transferred from one object to another through various means, such as friction or contact.

## What is the relationship between charge and electric fields?

Electric fields are created by charged particles and they exert forces on other charged particles. The strength of the electric field is directly proportional to the amount of charge present.

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