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The S-matrix is closely related to the transition probability amplitude in quantum mechanics and to cross sections of various interactions; the elements (individual numerical entries) in the S-matrix are known as scattering amplitudes. Poles of the S-matrix in the complex-energy plane are identified with bound states, virtual states or resonances.
In S-matrix theory, the S-matrix relates the infinite past to the infinite future in one step, without being decomposable into intermediate steps corresponding to time-slices. This program was very influential in the 1960s, because it was a plausible substitute for quantum field theory , which was plagued with the zero interaction phenomenon at ...
Within the canonical formulation of quantum field theory, a Feynman diagram represents a term in the Wick's expansion of the perturbative S-matrix. Alternatively, the path integral formulation of quantum field theory represents the transition amplitude as a weighted sum of all possible histories of the system from the initial to the final state ...
The Scattering transfer parameters or T-parameters of a 2-port network are expressed by the T-parameter matrix and are closely related to the corresponding S-parameter matrix. However, unlike S parameters, there is no simple physical means to measure the T parameters in a system, sometimes referred to as Youla waves.
where f ℓ is the partial scattering amplitude and P ℓ are the Legendre polynomials. The partial amplitude can be expressed via the partial wave S-matrix element S ℓ ( = e 2 i δ ℓ {\displaystyle =e^{2i\delta _{\ell }}} ) and the scattering phase shift δ ℓ as
Crossing states that the same formula that determines the S-matrix elements and scattering amplitudes for particle to scatter with and produce particle and will also give the scattering amplitude for + ¯ + to go into , or for ¯ to scatter with to produce + ¯. The only difference is that the value of the energy is negative for the antiparticle.
The transition amplitude is then given as the matrix element of the S-matrix between the initial and final states of the quantum system. Feynman used Ernst Stueckelberg's interpretation of the positron as if it were an electron moving backward in time. [3] Thus, antiparticles are represented as moving backward along the time axis in Feynman ...
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. [1] [2] [3] In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. [2]