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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.
But in the guise of string theory, S-matrix theory is still a popular approach to the problem of quantum gravity. The S-matrix theory is related to the holographic principle and the AdS/CFT correspondence by a flat space limit. The analog of the S-matrix relations in AdS space is the boundary conformal theory. [1]
The S-parameter for a 1-port network is given by a simple 1 × 1 matrix of the form () where n is the allocated port number. To comply with the S-parameter definition of linearity, this would normally be a passive load of some type.
This can be related to the 's if one uses the S-matrix to swap the two 's. Identifying the coefficients of the ϕ {\displaystyle \phi } 's on both sides of the equation one finds the desired formula relating S to the potential S a b = δ ( a − b ) − 2 i π δ ( E a − E b ) ( ϕ a , V ψ b + ) . {\displaystyle S_{ab}=\delta (a-b)-2i\pi ...
In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. [1] At large distances from the centrally symmetric scattering center, the plane wave is described by the wavefunction [ 2 ]
In quantum field theory, the Lehmann–Symanzik–Zimmermann (LSZ) reduction formula is a method to calculate S-matrix elements (the scattering amplitudes) from the time-ordered correlation functions of a quantum field theory.
Different fields of application have different definitions for the term. All the meanings are very similar in concept: In chemistry, the transmission coefficient refers to a chemical reaction overcoming a potential barrier; in optics and telecommunications it is the amplitude of a wave transmitted through a medium or conductor to that of the incident wave; in quantum mechanics it is used to ...
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 ...