Identical particles and Feynman diagrams

In summary, In Introduction to QFT (peskin) 4.5, the author mentions that the computation for M will be different when identical particles are present. However, in the first part of the book, there is no special treatment for identical particles. To compute M in this case, one must divide by a combinatorial factor, which can be found in the Feynman rules section. This factor takes into account the different contributions from Feynman diagrams when the particles are identical.
  • #1
taishizhiqiu
63
4
In Introduction to QFT (peskin) 4.5, he writes:

The computation for M, of course, will be quite different when identical particles are present.

However, I have finished reading the first part of the book and found no special treatment for identical particles. Can anybody tell me how to compute M if identical particles are present?
 
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  • #2
There is a combinatorial factor you must divide by when computing the amplitude for a scattering process involving identical particles. It's in the Feynman rules so look in the index for the section on them.
 
  • #3
WannabeNewton said:
There is a combinatorial factor you must divide by when computing the amplitude for a scattering process involving identical particles. It's in the Feynman rules so look in the index for the section on them.

But that's not about computing M matrix. So basically there's nothing special for identical particles?
 
  • #4
Different Feynman diagrams contribute if the particles are identical. For example, electron-muon scattering has only one diagram at tree level (t-channel photon exchange), but electron-electron scattering has two (t-channel and u-channel photon exchange).
 

1. What are identical particles?

Identical particles are particles that cannot be distinguished from one another based on their physical properties, such as mass, charge, or spin. This means that if two identical particles are in the same state, it is impossible to tell which particle is which.

2. Why is it important to consider identical particles in physics?

In quantum mechanics, identical particles play a crucial role in determining the behavior of systems. The properties and interactions of identical particles are described by the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state. This principle has important implications in understanding the behavior of matter at the atomic and subatomic level.

3. What are Feynman diagrams and how are they related to identical particles?

Feynman diagrams are graphical representations of mathematical expressions used to calculate the probability of various interactions between particles. They are used to visualize the behavior of identical particles in quantum field theory. Feynman diagrams help to simplify and visualize complex equations and calculations, making it easier to understand the behavior of identical particles in different scenarios.

4. How are identical particles represented in Feynman diagrams?

In Feynman diagrams, identical particles are represented by lines with arrows pointing in different directions. These lines can represent particles or antiparticles, depending on the direction of the arrow. Identical particles are also represented by the same type of line, indicating their identical properties.

5. What are some real-world applications of identical particles and Feynman diagrams?

Identical particles and Feynman diagrams are used extensively in various fields of physics, such as particle physics, condensed matter physics, and quantum computing. They are crucial in understanding the behavior of matter at the atomic and subatomic level and have practical applications in technology, such as in the development of transistors and computer memory devices.

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