Register to reply

Color factor

by spookyfish
Tags: color, factor
Share this thread:
spookyfish
#1
Apr8-14, 10:07 PM
P: 53
Hi. I was reading Griffiths page 289 and I wasn't sure how the transition from Eq. (8.45) to (8.46) was allowed. What bothers me is factoring out the "color factors" since the c's are vectors, and generally the elements of these color factors are matrices. For example, how is it allowed to pull out [itex]c_3^\dagger \lambda^\alpha c_1[/itex] out of [itex] \bar{u}(3)c_3^\dagger \lambda^\alpha \gamma^\mu u(1) c_1 [/itex]. Is it because the color factors live in a different space (color space) so they commute with spinor-space matrices?
Phys.Org News Partner Physics news on Phys.org
New complex oxides could advance memory devices
Nature's designs inspire research into new light-based technologies
UCI team is first to capture motion of single molecule in real time
Einj
#2
Apr8-14, 10:30 PM
P: 328
Yes, the color vectors [itex]c_i[/itex] live in a space different from that of the Dirac spinors [itex]u(i)[/itex]. If you still feel uncomfortable you can always use explicit indices: the Dirac spinors and the Dirac matrices have indices, say, i,j,k and the color vectors and the color generators have indices, say, a,b,c. Once the indices are explicit all the quantities commute with each other since they are just numbers. Then, for example:
$$
\bar u(3)c_3^\dagger\lambda^\alpha\gamma_\mu u(1)c_1=\bar u_i(3)c_{3a}^\dagger\lambda^\alpha_{ab}\gamma_{\mu}^{ij}u_j(1)c_{1b}= \bar u_i(3)\gamma_\mu^{ij}u_j(1)c_{3a}^\dagger\lambda_{ab}^\alpha c_{1b}=(\bar u(3)\gamma_\mu u(1))(c_3^\dagger\lambda^\alpha c_1).
$$
I hope this answer your question.
spookyfish
#3
Apr9-14, 07:20 PM
P: 53
yes, thank you


Register to reply

Related Discussions
Calculating Color temperature and Color Rendering Index.. General Physics 9
Plotting a Color Graph with Mathematica [x vs y and z as the color] Math & Science Software 0
Questions about the gluons, their color and anti-color charges and charge of quarks High Energy, Nuclear, Particle Physics 15
Mathematica PlotStyle->{color,color,color} not working Math & Science Software 3
Extraterrestrial sky color based on atmospheric composition and sun color Astronomy & Astrophysics 4