# Feynman diagrams from Quarks and Leptons Halzen and Martin?

• Spinnor
In summary, the difference between figure (b) and (c) in the Feynman diagrams from "Quarks and Leptons" by Halzen and Martin is that (c) includes additional information about the color index of the fields, while (b) does not. This is due to the fact that in QCD, gluons have a color index and are charged under the corresponding interaction, while photons do not have a color-like index and are neutral under the EM interaction. This is represented by the use of a double line in (c) for gluons.
Spinnor
Gold Member
Feynman diagrams from "Quarks and Leptons" Halzen and Martin?

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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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.

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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Spinnor said:
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.

## 1. What are Feynman diagrams and how do they relate to quarks and leptons?

Feynman diagrams are graphical representations of particle interactions in quantum field theory. They were developed by physicist Richard Feynman and are used to visualize and calculate the probability of particle interactions. Quarks and leptons are fundamental particles that make up the building blocks of matter, and their interactions can be represented by Feynman diagrams.

## 2. How do Feynman diagrams help us understand the behavior of quarks and leptons?

Feynman diagrams allow us to visualize and calculate the probability of particle interactions, which helps us understand the behavior of quarks and leptons. By studying the patterns and outcomes of these interactions, we can gain insight into the fundamental laws of nature that govern the behavior of these particles.

## 3. What is the significance of the different lines and symbols in Feynman diagrams?

The lines in Feynman diagrams represent the paths of particles, with straight lines representing fermions (such as quarks and leptons) and wavy lines representing bosons (such as photons). The symbols at the ends of the lines represent the type of particle involved in the interaction, and the arrows indicate the direction of the interaction.

## 4. How are Feynman diagrams used in particle physics research?

Feynman diagrams are an essential tool in particle physics research. They are used to calculate the probabilities of particle interactions, which can then be compared to experimental data. By analyzing the patterns and outcomes of these interactions, scientists can test and refine theories about the fundamental laws of nature.

## 5. Can Feynman diagrams be used to study other particles besides quarks and leptons?

Yes, Feynman diagrams can be used to study other particles, such as gauge bosons, Higgs bosons, and other hypothetical particles. They are a versatile tool for studying the behavior and interactions of all types of particles in quantum field theory.

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