S-Matrix in Quantum Field Theory

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• gremory
In summary, the S-matrix can be used to compute the scattering amplitude of certain processes. However, learning how to use it effectively requires studying a textbook on S-matrix theory. It is not something that can be taught in a PF thread.
gremory
TL;DR Summary
Usage of the S-matrix
Hello, i need help with the S-matrix. From what i understand, with the S-matrix i would be able to compute the scattering amplitude of some processes, is that correct? If so, how would i be able to do that if i have some field ##\phi(x,t)## in hands? Is that possible?

Study Peskin & Schroeder...

gremory said:
i need help with the S-matrix.
That is more help than is within the scope of a PF thread. You are basically asking for a course in S matrix theory, and for that you need a textbook (such as the one @strangerep suggested), not a PF thread.

gremory said:
From what i understand, with the S-matrix i would be able to compute the scattering amplitude of some processes, is that correct?
Yes. However...

gremory said:
If so, how would i be able to do that if i have some field ##\phi(x,t)## in hands? Is that possible?
It's certainly possible, but as above, learning how to do it takes one or more full-time courses in S-matrix theory. It's not something we're going to be able to teach you in a PF thread.

If, after taking some time to study a textbook, you have particular questions about what you are reading, by all means open a new thread with a much more specific focus. In the meantime, this thread is closed.

vanhees71 and strangerep

1. What is the S-Matrix in Quantum Field Theory?

The S-Matrix, or scattering matrix, is a mathematical tool used in quantum field theory to describe how particles interact and scatter off of each other. It is defined as the matrix element of the time evolution operator between the initial and final states of a scattering process.

2. How is the S-Matrix calculated?

The S-Matrix is calculated by taking the product of all the individual scattering matrices for each particle interaction in a given process. This involves summing over all possible paths and interactions between particles, and can be a very complex and time-consuming calculation.

3. What is the significance of the S-Matrix in quantum field theory?

The S-Matrix is a powerful tool in quantum field theory as it allows for the calculation of scattering amplitudes, which are essential in understanding the behavior of particles and their interactions. It also provides a way to test the predictions of quantum field theories through experimental measurements.

4. Can the S-Matrix be used to describe all particle interactions?

No, the S-Matrix is limited to describing interactions between particles that are weakly interacting and can be treated as point particles. Strongly interacting particles, such as quarks and gluons, require other mathematical tools such as the path integral formulation to be described accurately.

5. How does the S-Matrix relate to other concepts in quantum field theory?

The S-Matrix is closely related to other important concepts in quantum field theory, such as Feynman diagrams and the renormalization process. It also plays a crucial role in the study of symmetries and conservation laws in particle interactions.

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