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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 most lasting legacy of the ...
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 quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products of field operators. They are a key object of study in quantum field theory where they can be used to calculate various observables such as S-matrix elements.
By expanding the S-matrix into a sum of a product of connected S-matrix elements , which at the perturbative level are equivalent to connected Feynman diagrams, the cluster decomposition property can be restated as demanding that connected S-matrix elements must vanish whenever some of its clusters of particles are far apart from each other.
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.
The S-matrix in quantum field theory is an example of a time-ordered product. The S-matrix, transforming the state at t = −∞ to a state at t = +∞, can also be thought of as a kind of "holonomy", analogous to the Wilson loop. We obtain a time-ordered expression because of the following reason: We start with this simple formula for the ...
In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform.The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary ...
In his paper "The S-Matrix in Quantum electrodynamics", [1] Dyson derived relations between different S-matrix elements, or more specific "one-particle Green's functions", in quantum electrodynamics, by summing up infinitely many Feynman diagrams, thus working in a perturbative approach.