# What is charge actually? How to define it? [closed]

Is charge of something for (e.g.) an electron related to electromagnetic space if it exists due to energy, due to which it may have mass? I don't know about quantum mechanics or advanced particle models. Can anyone just simply give an intuitive idea?

EDIT I want to mean what actually gives electron charge if it is not assumed fundamental but result of some other physical phenomenon or it is just the quantity defined to explain physical interactions?I think now it is clear

## closed as unclear what you're asking by John Rennie, Kyle Kanos, Brandon Enright, Jim, Emilio PisantyApr 3 '14 at 23:57

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• I'm unsure what you're after. Do you want to define it as your title says, or do you want an intuitive idea, as in your question text? – BMS Apr 3 '14 at 16:09
• – The Photon Apr 3 '14 at 20:34
• Duplicate of physics.stackexchange.com/q/57199 – Kyle Kanos Apr 4 '14 at 15:38

Charge is a fundamental conserved property of particles. It is, if you like, a measure of how much a particle interacts with electromagnetic fields. A particle with charge can produce and be affected by electromagnetic fields. This is what we mean when we say a particle has electric charge. It might help to think of it as a simple quantised way to measure the coupling strength of particles with the appropriate force, as the concept of charge extends to other forces as well.

e.g:

electric charge for electromagnetic force, colour charge for strong force, etc.

Please also see @JamalS's answer which is thicker on the abstraction and shows the quantum field theoretic origins of electric charge

Charge is a quantity which arises from Noether's theorem, due to continuous global symmetries (up to a total derivative) of a Lagrangian, and as such we have many types of charge, other than electric. For example, consider the Dirac Lagrangian,

$$\mathcal{L} = \bar{\psi}(i\gamma^{\mu}\partial_{\mu}-m)\psi$$

which describes fermions. It is invariant by a change of phase, i.e. $\psi \to e^{-i\alpha}\psi$, which has a conserved current, namely,

$$j^{\mu} = \bar{\psi}\gamma^\mu \psi$$

The conserved quantity, i.e. Noether charge, arising from the symmetry is the integral over all space of the zeroth component, therefore

$$Q = \int \mathrm{d}^3 x \, \, \bar{\psi} \gamma^0 \psi = \int \mathrm{d}^3 x \, \, \psi^{\dagger}\psi$$

The quantity $Q$ is indeed electric charge. In addition, when the field $\psi$ is quantized, and expanded as a plane wave with operators as Fourier coefficients, it can be shown that $Q$ also has the interpretation of particle number for fermions. In classical electromagnetism, charge also determines the magnitude of the effect of magnetic and electric fields on charged matter, via the Lorentz force relation,

$$\vec{F} = q\left(\vec{E}+ \vec{v} \times \vec{B}\right)$$

The elementary charge $e$ also plays the role of the coupling constant in quantum electrodynamics, which roughly determines the strength of an interaction term, namely,

$$\mathcal{L}_{\mathrm{int}} \sim e \bar{\psi}\gamma^\mu A_\mu \psi$$

corresponding to an interaction vertex involving a photon, positron and electron. In addition, the coupling $e$ actually depends on a scale, dictated by the beta function (to one loop order), $$\beta (e) = \frac{e^3}{12\pi^2}$$

So the idea that there is a single $e$ is wrong; from the beta function, assuming no additional corrections alter its nature, we may deduce the coupling increases with increasing energy scale.