Feynman diagrams from "Quarks and Leptons" Halzen and Martin?


by Spinnor
Tags: diagrams, feynman, halzen, martin, quarks and leptons
Spinnor
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Jan4-13, 07:19 PM
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The following scan is from Quarks and Leptons: An Introductory Course in Modern Particle Physics, Francis Halzen (Author), Alan D. Martin (Author), page 9. Can I take anything from the topological difference between figure (b) and (c)?

Thanks for any help!
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Bill_K
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Jan5-13, 06:18 AM
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Diagram (c) is not a Feynman diagram, just a way of illustrating the fact that color is exactly conserved. You can follow a continuous path that traces the B color, in one line and out the other. A gluon carries color and anti-color, so the two lines in the middle of the diagram both belong to the same gluon.
Spinnor
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Jan8-13, 06:58 PM
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Referring to the scan above, does there exist a new diagram that could have been included in the book "Quarks and Leptons", call it figure (e), such that,

Figure (b) is to figure (c) as figure (a) is to figure (e)? See figure (e) below.

If so can we think that the photon is equal opposite currents that cancel perfectly or nearly perfectly?

Thanks for any help!
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fzero
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Jan8-13, 11:39 PM
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Feynman diagrams from "Quarks and Leptons" Halzen and Martin?


Quote Quote by Spinnor View Post
Referring to the scan above, does there exist a new diagram that could have been included in the book "Quarks and Leptons", call it figure (e), such that,

Figure (b) is to figure (c) as figure (a) is to figure (e)? See figure (e) below.

If so can we think that the photon is equal opposite currents that cancel perfectly or nearly perfectly?

Thanks for any help!
The photon is not composed of equal opposite currents and neither is the gluon. As Bill_K said, the diagrams of the type (c) include additional information about the color index of the fields. In QCD (an example of a so-called non-abelian gauge theory), the gluon has a color index and is therefore charged under the corresponding interaction. To further understand the difference requires some group theory. Simply put, in terms of color-components, quarks and antiquarks are like vectors, while gluons are matrices. Gluons then carry a pair of indices, so it makes sense to draw them with a double line in (c). Photons do not have a color-like index (QED is a U(1) or abelian gauge theory), so there is no reason to draw a diagram analogous to (c). The lack of a gauge index corresponds to the fact that photons are neutral under the EM interaction.


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