In theoretical physics, crossing symmetry is a relation between the S-matrix that describe processes that can be obtained from each other by replacing incoming particles with outgoing antiparticles after taking the analytic continuation. For example, the annihilation of an electron with a positron into two photons is related to an elastic scattering of an electron with a photon by crossing symmetry. This relation allows to calculate the scattering amplitude of one process from the amplitude for the other process if negative values of energy of some particles are substituted. Theoretical physics is physics that employs mathematical models and abstractions rather than experimental processes. ... The S-matrix is the matrix in quantum mechanics, scattering theory or quantum field theory that relates the final state in the infinite future ( out channels) and the initial state in the infinite past ( in channels). ... In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of definition of a given analytic function. ... Annihilation is defined as total destruction or complete obliteration of a particular object. ... Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... In physics, the photon (from Greek φως phos, meaning light) is a quantum of the electromagnetic field, for instance light. ... In scattering theory and in particular in particle physics, elastic scattering is one of the specific forms of scattering. ... The S-matrix is the matrix in quantum mechanics or quantum field theory that relates the final state in the infinite future and the initial state in the infinite past. ...
Crossing symmetry exists because of the Wick rotation. In physics, a Wick rotation is the process by which a theory in Euclidean space is analytically continued into one in Minkowski space and vice versa. ...
The triangles with this symmetry are isosceles, the quadrilaterals with this symmetry are the geometric kites and the isosceles trapezoids.
Symmetry is used in the design of the overall floor plan of buildings as well as the design of individual building elements such as doors, windows, floors, frieze work, and ornamentation; many facades adhere to bilateral symmetry.
Symmetry is also an important consideration in the formation of scales and chords, traditional or tonal music being made up of non-symmetrical groups of pitches, such as the diatonic scale or the major chord.
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