Search results
Results from the WOW.Com Content Network
Axial symmetry is symmetry around an axis or line (geometry). An object is said to be axially symmetric if its appearance is unchanged if transformed around an axis. The main types of axial symmetry are reflection symmetry and rotational symmetry (including circular symmetry for plane figures). [ 1 ]
The chiral symmetry transformation can be divided into a component that treats the left-handed and the right-handed parts equally, known as vector symmetry, and a component that actually treats them differently, known as axial symmetry. [2] (cf. Current algebra.) A scalar field model encoding chiral symmetry and its breaking is the chiral model.
de Valcourt (1966) lists 11 different measures of axial symmetry, of which the one described here is number three. [8] He requires each such measure to be invariant under similarity transformations of the given shape, to take the value one for symmetric shapes, and to take a value between zero and one for other shapes. Other symmetry measures ...
Likewise, if a theory possesses an internal chiral or axial symmetry, there will be a conserved quantity, which is called the axial charge. Further, just as the motion of an electrically charged particle produces an electric current , a moving axial charge constitutes an axial current.
C i (equivalent to S 2) – inversion symmetry; C 2 – 2-fold rotational symmetry; C s (equivalent to C 1h and C 1v) – reflection symmetry, also called bilateral symmetry. Patterns on a cylindrical band illustrating the case n = 6 for each of the 7 infinite families of point groups. The symmetry group of each pattern is the indicated group.
This, when the proper axial SU(2) symmetry is included, is the Gell-Mann Levy σ-model, discussed below. The modern explanation for the shift symmetry is now understood to be the Nambu-Goldstone non-linear symmetry realization mode, due to Yoichiro Nambu [3] and Jeffrey Goldstone.
The Standard Model exhibits a (−1) F symmetry, where F is the fermion number operator counting how many fermions are in a state. Since all particles in the Standard Model satisfy F = B + L, the discrete symmetry is also part of the e iα(B + L) continuous symmetry group.
The axial pieces of these symmetries are spontaneously broken so that the corresponding scalar fields are the requisite Nambu−Goldstone bosons. The model was later studied in the two-dimensional case as an integrable system, in particular an integrable field theory.