Why are disconnected diagrams dropped from S-Matrix

In summary, when calculating elements of correlation functions in perturbative quantum field theory, connected and disconnected diagrams are often encountered. These disconnected diagrams are typically dropped from the calculation, even though they may contribute to the same process and exhibit quantum interference. This is because the interferences are eliminated when averaging over the relative temporal and spatial separation of the scattering events, resulting in a simple product of the averaged S-matrix contribution.
  • #1
LedPhoton
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I am talking about perturbative quantum field theory. When calculating elements of correlation functions(which then I use to calculate S-matrix elements) one always comes up with connected and disconnected diagrams. These disconnected diagrams are usually dropped from the calculation and I wonder why. Note that I am not talking about vacuum-vacuum diagrams.
I'll give an example, suppose you have real scalar field with a Phi^3 interaction AND a Phi^6 interaction. A 2Phi->4Phi particle scattering can happen in at least two ways (as calculated from a six point correlating function):
One 6-point vertex in which 2 initial particles enter and 4 final particles exit.
Two 3-point vertex. In each vertex 1 initial particle enters and 2 final particles exit.
It seems to be tacitly assumed that the second diagram may be dropped. In most cases we may understand these to be two separate processes, but there must be some cases in which the two terms contribute to the same process: there must be quantum interference between the terms.
Is there some process that kills this interference? Why is the disconnected diagram usually dropped?
Thanks
 
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  • #2
I am not an expert on this, but I remember that the interferences drop out as you average over the relative temporal/ spatial separation of the scattering events. You finally get a simple product of the averaged S-matrix contribution.
 

1. Why are disconnected diagrams dropped from S-Matrix?

The S-Matrix is a mathematical tool used in particle physics to calculate the probabilities of different particle interactions. Disconnected diagrams, which represent interactions between two or more particles that do not interact with each other, are typically dropped from the S-Matrix because they do not contribute significantly to the overall probability. This simplifies the calculation and makes it more accurate.

2. How are disconnected diagrams identified in the S-Matrix?

Disconnected diagrams are identified by looking at the Feynman diagrams used to represent particle interactions. If there is no direct connection between the particles in the diagram, it is considered a disconnected diagram and is typically dropped from the S-Matrix calculation.

3. Can disconnected diagrams ever be included in the S-Matrix?

In some cases, disconnected diagrams may be included in the S-Matrix calculation if they contribute significantly to the overall probability. This is more common in high-energy interactions or when studying specific types of interactions. However, in most cases, disconnected diagrams are dropped to simplify the calculation.

4. How does dropping disconnected diagrams affect the accuracy of the S-Matrix?

Dropping disconnected diagrams from the S-Matrix does not significantly affect the accuracy of the calculation. The contribution of these diagrams is usually very small compared to other diagrams, and their exclusion leads to a more precise result. However, in some cases, these diagrams may be important and should not be dropped.

5. Are there any other reasons why disconnected diagrams are dropped from the S-Matrix?

Aside from simplifying the calculation and improving accuracy, another reason for dropping disconnected diagrams from the S-Matrix is to avoid double-counting. Some particles may interact with each other multiple times, and including all possible diagrams would lead to overcounting and incorrect results. By dropping disconnected diagrams, this issue is avoided.

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