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In summary, the S matrix assumes that interacting particles are free and that the vacuum is not an important factor in the theory.

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Physics news on Phys.org

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Mentor

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So from the point of view of the S matrix, an interacting particle with momentum p and a non-interacting particle with momentum p are identical at ##\pm \infty##? But the operators used to create a particle with momentum p i.e. ##a_p^\dagger## is different (they evolve differently in time) in the 2 theories as the vacuum is different?mfb said:

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This may be of interest to you https://en.m.wikipedia.org/wiki/Haag's_theorem

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The conceptual framework of QFT, Oxford University Press

It's precisely filling the gaps Weinberg's three volumes leave.

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Page 3 said:'the description of such a process as occurring in the course of time is therefore just as unreal as the classical paths are in non-relativistic quantum mechanics. The only observable quantities are the properties of free particles'

An S matrix, also known as the scattering matrix, is a mathematical tool used in physics to describe the scattering of particles or waves. It relates the incoming and outgoing states of a system and is often used to analyze the interaction between particles or fields.

The S matrix is used to calculate the probability of a particle or wave scattering off a potential. In the case of vanishing fields, the potential is zero, meaning there is no interaction between the incoming and outgoing particles or waves. Therefore, the S matrix for vanishing fields is simply the identity matrix, as there is no scattering or change in the state.

Yes, the S matrix can be used to study quantum systems, particularly in the field of quantum mechanics. It is a key tool in understanding the behavior of particles at the quantum level and is used to calculate various observables, such as cross-sections and decay rates.

The S matrix is calculated using the principles of quantum mechanics and relies on the use of mathematical techniques such as perturbation theory and Feynman diagrams. The exact method of calculation depends on the specific system being studied and the level of accuracy required.

The S matrix has various applications in different fields of physics, such as nuclear physics, particle physics, and quantum field theory. It is used in the study of scattering processes, particle decays, and the behavior of quantum systems. It also has practical applications in engineering, such as in the design of electronic circuits and antennas.

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