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scattering and string
This is accomplished at the level of perturbation theory by finding a collection of vertices for joining and splitting strings, as well as string propagators, that give a Feynman diagram-like expansion for string scattering amplitudes.
The principal advantages of the formalism are that it allows the computation of off-shell amplitudes and, when a classical action is available, gives non-perturbative information that cannot be seen directly from the standard genus expansion of string scattering.
String field theories come in a number of varieties depending on which type of string is second quantized: Open string field theories describe the scattering of open strings, closed string field theories describe closed strings, while open-closed string field theories include both open and closed strings.
Light-cone string field theories were the first string field theories to be constructed and are based on the simplicity of string scattering in light-cone gauge.
For example, in the bosonic closed string case, the worldsheet scattering diagrams naturally take a Feynman diagram-like form, being built from two ingredients, a propagator,
These vertices and propagators produce a single cover of the moduli space of-point closed string scattering amplitudes so no higher order vertices are required.
These Feynman diagrams generate a complete cover of the moduli space of open string scattering diagrams.
If one demands that on-shell scattering diagrams be reproduced to all orders in the string coupling, one must also include additional vertices arising from higher genus ( and hence higher order in ) as well.
For example, twistor string theory may simplify calculating scattering amplitudes from Feynman diagrams.
This induces open string production and as a result the two scattering branes will be trapped.
In the case of a Tonks – Girardeau gas ( TG ), so many properties of this one-dimensional string of bosons would be sufficiently fermion-like that the situation is often referred to as the ' fermionization ' of bosons. Tonks – Girardeau gas coincide with quantum Nonlinear Schrödinger equation for infinite repulsion, which can be efficiently analyzed by Quantum inverse scattering method.
After many false starts, Dolen Horn and Schmidt understood a crucial property that led Gabriele Veneziano to formulate a self-consistent scattering amplitude, the first string theory.
Although the S-matrix approach to the strong interactions was largely abandoned by the particle physics community in the 1970s in favor of quantum chromodynamics, a consistent theory for the scattering of bound-states on straight-line trajectories was eventually constructed and is nowadays known as string theory.

scattering and theory
In the complementary energy-dependent approach, the time-independent Schrödinger equation is solved using the scattering theory formalism.
* Small angle scattering theory of fractally rough systems
The full theory does not yet have a satisfactory definition in all circumstances, since the scattering of strings is most straightforwardly defined by a perturbation theory.
And he proposed a theory that they were produced in interstellar space as by-products of the fusion of hydrogen atoms into the heavier elements, and that secondary electrons were produced in the atmosphere by Compton scattering of gamma rays.
Typically, the theory and applications of emission, absorption, scattering of electromagnetic radiation ( light ) from excited atoms and molecules, analysis of spectroscopy, generation of lasers and masers, and the optical properties of matter in general, fall into these catergories.
Thomson scattering, the classical theory of an electromagnetic wave scattered by charged particles, cannot explain low intensity shifts in wavelength.
Experimental verification of momentum conservation in individual Compton scattering processes by Bothe and Geiger as well as by Compton and Simon has been important in disproving the BKS theory.
In zero order dynamical theory of diffraction the refractive index is directly related to the scattering length density and is a measure of the strength of the interaction of a neutron wave with a given nucleus.
The effects of such features on the path of almost any type of propagating wave or moving particle can be described in the framework of scattering theory.
Some areas where scattering and scattering theory are significant include radar sensing, medical ultrasound, semiconductor wafer inspection, polymerization process monitoring, acoustic tiling, free-space communications, and computer-generated imagery.
Scattering theory is a framework for studying and understanding the scattering of waves and particles.
In the Mie regime, the shape of the scattering center becomes much more significant and the theory only applies well to spheres and, with some modification, spheroids and ellipsoids.
In order to model weather systems, atmospheric physicists employ elements of scattering theory, wave propagation models, cloud physics, statistical mechanics and spatial statistics which are highly mathematical and related to physics.
He studied probability theory, the scattering of electrons, and the discharges of electric eels.
* Mie theory or Mie scattering, a solution of Maxwell's equations for the scattering of electromagnetic radiation
( See Feshbach – Fano partitioning method for the context where such operators appear in scattering theory ).
At larger values of the ratio of particle diameter to wavelength, the scattering varies in a complex fashion described, for spherical particles, by the Mie theory ; at a ratio of the order of 10, the laws of geometric optics begin to apply.

scattering and can
All these phenomena, molecular absorption and radiation scattering, can result in artificially high absorption and an improperly high ( erroneous ) calculation for the concentration or mass of the analyte in the sample.
In all of these cases in nature, the same brilliant iridescence ( or play of colors ) can be attributed to the diffraction and constructive interference of visible lightwaves that satisfy Bragg ’ s law, in a matter analogous to the scattering of X-rays in crystalline solids.
Neutrons can also probe atomic length scales and are used to study scattering off nuclei and electron spins and magnetization ( as neutrons themselves have spin but no charge ).
Coulomb and Mott scattering measurements can be made by using electron beams as scattering probes, and similarly, positron annihilation can be used as an indirect measurement of local electron density.
Together with particle density and path length, it can be used to predict the total scattering probability via the Beer-Lambert law.
ARPES can be used to determine the direction, speed and scattering of electrons within the material.
When calculating scattering cross sections in particle physics, the interaction between particles can be described by starting from a free field which describes the incoming and outgoing particles, and including an interaction Hamiltonian to describe how the particles deflect one another.
For instance, diamagnetism, birefringence, Raman scattering, NMR and EPR can also be used to determine S.
However, blurring is not caused by random processes, such as light scattering, but can be well defined by the optical properties of the image formation in the microscope imaging system.
Perfectly elastic " collisions " can occur when the objects do not touch each other, as for example in atomic or nuclear scattering where electric repulsion keeps them apart.
A neutron on its own is unstable ( see below ), but they can be found in nuclear reactions ( see neutron radiation ) and are used in scientific analysis ( see neutron scattering ).
Rayleigh scattering can be defined as scattering in the small size parameter regime.
The amount of Rayleigh scattering from a single particle can also be expressed as a cross section σ.
Some of the scattering can also be from sulfate particles.
λ < sup >− 4 </ sup > Rayleigh-type scattering can also be exhibited by porous materials.
There exist other physical processes that can lead to a shift in the frequency of electromagnetic radiation, including scattering and optical effects ; however, the resulting changes are distinguishable from true redshift and not generally referred as such ( see section on physical optics and radiative transfer ).
The energy exchange between the electron beam and the sample results in the reflection of high-energy electrons by elastic scattering, emission of secondary electrons by inelastic scattering and the emission of electromagnetic radiation, each of which can be detected by specialized detectors.
Similar diffraction patterns can be produced by scattering electrons or neutrons, which are likewise interpreted as a Fourier transform.
If single crystals of sufficient size cannot be obtained, various other X-ray methods can be applied to obtain less detailed information ; such methods include fiber diffraction, powder diffraction and small-angle X-ray scattering ( SAXS ).

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