Chiral model
Encyclopedia
In nuclear physics
, the chiral model is a phenomenological model describing meson
s in the chiral limit where the masses of the quark
s go to zero (without mentioning quarks at all). It's a nonlinear sigma model with the principal homogeneous space
of the Lie group
SU(N)
as its target manifold where N is the number of quark flavor
s. The Riemannian metric of the target manifold is given by a positive constant multiplied by the Killing form
acting upon the Maurer-Cartan form
of SU(N). The internal global symmetry
of this model is SU(N)L×SU(N)R, the left and right copies respectively where the left copy acts as the left action
upon the target space and the right copy acts as the right action
. The left copy describes rotations among the left-handed quarks while the right copy describes rotations among the right-handed quarks and they are independent of each other. This model admits topological solitons called Skyrmion
s.
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
, the chiral model is a phenomenological model describing meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s in the chiral limit where the masses of the quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s go to zero (without mentioning quarks at all). It's a nonlinear sigma model with the principal homogeneous space
Principal homogeneous space
In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G such that the stabilizer subgroup of any point is trivial...
of the Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
SU(N)
Special unitary group
The special unitary group of degree n, denoted SU, is the group of n×n unitary matrices with determinant 1. The group operation is that of matrix multiplication...
as its target manifold where N is the number of quark flavor
Flavor
Flavor or flavour is the sensory impression of a food or other substance, and is determined mainly by the chemical senses of taste and smell. The "trigeminal senses", which detect chemical irritants in the mouth and throat as well as temperature and texture, are also very important to the overall...
s. The Riemannian metric of the target manifold is given by a positive constant multiplied by the Killing form
Killing form
In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and Lie algebras...
acting upon the Maurer-Cartan form
Maurer-Cartan form
In mathematics, the Maurer–Cartan form for a Lie group G is a distinguished differential one-form on G that carries the basic infinitesimal information about the structure of G...
of SU(N). The internal global symmetry
Global symmetry
A global symmetry is a symmetry that holds at all points in the spacetime under consideration, as opposed to a local symmetry which varies from point to point.Global symmetries require conservation laws, but not forces, in physics.-See also:...
of this model is SU(N)L×SU(N)R, the left and right copies respectively where the left copy acts as the left action
Group action
In algebra and geometry, a group action is a way of describing symmetries of objects using groups. The essential elements of the object are described by a set, and the symmetries of the object are described by the symmetry group of this set, which consists of bijective transformations of the set...
upon the target space and the right copy acts as the right action
Group action
In algebra and geometry, a group action is a way of describing symmetries of objects using groups. The essential elements of the object are described by a set, and the symmetries of the object are described by the symmetry group of this set, which consists of bijective transformations of the set...
. The left copy describes rotations among the left-handed quarks while the right copy describes rotations among the right-handed quarks and they are independent of each other. This model admits topological solitons called Skyrmion
Skyrmion
In theoretical physics, a skyrmion is a mathematical model used to model baryons . It was conceived by Tony Skyrme.-Overview:...
s.