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

by nouveau_riche
Tags: charge, kind
 P: 253 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?
 P: 117 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.
 Sci Advisor P: 5,295 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.
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## what is charge? i do not want to hear that it is of two kind

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.
 Sci Advisor P: 5,295 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!
P: 253
 Quote by conquest 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
P: 253
 Quote by tom.stoer 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

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