Why do they only consider S-matrix in QFT?

In summary, the S-matrix is the most fundamental tool in quantum field theory (QFT) as it allows for the calculation of probabilities of particle interactions. It is advantageous in QFT due to its unitary properties and close relation to Feynman diagrams. However, it may have limitations when describing processes involving the creation or annihilation of particles, and its applicability may be limited in certain cases.
  • #1
ndung200790
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Please teach me this:
Why do they only consider S-matrix(or Green functions) in Quantum Field Theory?How about other physics observations as considering in normal Quantum Mechanics,e.g angular momentum...of particles?If we consider the other physical observations,how could we represent them in language of Quantum Field Theory?
Thank you very much in advance.
 
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  • #2
ndung, Scattering cross-sections are a main focus of calculations in quantum field theory because most experiments are scattering experiments. There are plenty of other calculations too which are not related to scattering: linewidths and lifetimes, anomalous magnetic moment, Lamb shift, etc
 

1. Why is the S-matrix the only tool used in QFT calculations?

The S-matrix is the most fundamental tool in quantum field theory (QFT) because it describes the scattering of particles, which is the main focus of QFT. It allows us to calculate the probabilities of different particle interactions, which is essential for understanding the behavior of quantum systems.

2. What are the advantages of using the S-matrix in QFT?

One of the main advantages of using the S-matrix in QFT is that it is a unitary operator, meaning that it preserves the total probability of all possible outcomes. This is essential for maintaining the consistency of the theory and ensuring that the predictions made by QFT are accurate.

3. How does the S-matrix relate to other concepts in QFT, such as Feynman diagrams?

The S-matrix is closely related to Feynman diagrams, as they both represent the scattering of particles. In fact, the S-matrix elements can be calculated using Feynman diagrams, making them a powerful tool for understanding the behavior of quantum systems.

4. Are there any limitations to using the S-matrix in QFT?

The S-matrix has some limitations, particularly when it comes to describing processes that involve the creation or annihilation of particles. In these cases, other tools such as the LSZ reduction formula may be used in conjunction with the S-matrix to obtain more accurate results.

5. Can the S-matrix be applied to all quantum systems?

The S-matrix is most commonly used in QFT, but it can also be applied to other quantum systems, such as quantum mechanics and quantum statistical mechanics. However, its applicability may be limited in certain cases, such as systems with strong interactions or in the presence of external forces.

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