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What is charge? i do not want to hear that it is of two kind 
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#1
Mar1112, 08:36 AM

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? 


#2
Mar1112, 10:59 AM

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. 


#3
Mar1212, 01:56 AM

Sci Advisor
P: 5,366

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. [tex]Q = e\int_{\mathbb{R}^3}d^3x\,\rho(x) [/tex] [tex]\frac{dQ}{dt} = 0[/tex] 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: [tex]\rho = j^0 = \psi^\dagger \psi[/tex] Again Q is defined as an integral and is conserved, i.e. [tex][H,Q] = 0[/tex] 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. [tex]Q\psi\rangle = q\psi\rangle = ne\psi\rangle[/tex] 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 [tex]\psi\rangle = n=1\rangle + n=2\rangle;\;\;Qn\rangle = nn\rangle[/tex] must not exist. 


#4
Mar1212, 08:00 AM

P: 603

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.



#5
Mar1312, 02:14 AM

Sci Advisor
P: 5,366

there are some reasons (especially in nonabelian gauge theories) that total charge is always zero for physical states, i.e. Qphys> = 0, but this is not completely rigorous; note: in QCD is colorneutrality is different from colorconfinement!



#6
Mar1312, 09:34 AM

P: 253




#7
Mar1312, 09:35 AM

P: 253




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