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ψ in formula for strong force currents, how many components? 
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#1
Dec2113, 10:45 AM

P: 1,368

In the ψ below, there are 4 components for the Dirac spinnor times three possible color states for a total of 12 components for ψ?
Thanks for any help! Thanks to ChrisVer for the original post! 


#2
Dec2213, 05:53 PM

Thanks
P: 1,948

No, color confinement prevents anything like a classical color current.



#3
Dec2213, 09:39 PM

P: 844

##j^{a \mu} = \bar \psi_{\alpha i} \gamma^\mu_{\alpha \beta} \lambda^a_{ij} \psi_{\beta j}## Here ##\alpha## and ##\beta## are Dirac indices, which take on four possible values; ##i## and ##j## are indices for the fundamental representation of SU(3), and take on three possible values; ##a## is an index for the adjoint representation of SU(3), and takes on eight possible values; and ##\mu## is a Lorentz index and takes on four possible values. ##j^{a0}## is the color charge density and ##j^{a\mu}##, ##\mu = 1, 2, 3## is the color current density. 


#4
Dec2313, 06:43 AM

P: 1,368

ψ in formula for strong force currents, how many components?
At high energies in a quark/gluon plasma does need for colorless combinations of quarks and antiquarks still apply? Thanks for the help! 


#5
Dec2313, 06:49 AM

P: 1,368

Can the above sum be simply realized as a single multicomponent matrix sandwiched between two multicomponent vectors? Thanks for your help! 


#6
Dec2313, 03:04 PM

P: 844




#7
Dec2313, 03:23 PM

P: 754

Is that true Duck? I mean it'd be like breaking the tensor product of representations into tensor sum



#8
Dec2313, 04:20 PM

Thanks
P: 1,948




#9
Dec2313, 06:08 PM

P: 844

[tex]\sigma_3 \otimes \sigma_3 = \left(\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}\right)[/tex] [tex]\sigma_1 \otimes \sigma_1 = \left(\begin{array}{cccc} 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{array}\right)[/tex] Similarly ##\gamma^\mu \lambda^a## can in principle be thought of as a ##12 \times 12## matrix acting on the dimension12 tensor product representation that ##\psi## lives in. 


#10
Dec2413, 04:39 AM

P: 1

what happens to electrons in nuclear reaction ?



#11
Dec2413, 08:16 AM

P: 1,368

http://en.wikipedia.org/wiki/File:Be...tive_Decay.svg http://en.wikipedia.org/wiki/W_and_Z..._nuclear_force 


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