Search results
Results from the WOW.Com Content Network
In physical terms, a spinor should determine a probability amplitude for the quantum state. A manner of regarding the product ψ ϕ as a vector. This is an essential feature of Dirac's theory, which ties the spinor formalism to the geometry of physical space. A manner of regarding a spinor as acting upon a vector, by an expression such as ψv ψ.
In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos.It appears in the plane-wave solution to the Dirac equation, and is a certain combination of two Weyl spinors, specifically, a bispinor that transforms "spinorially" under the action of the Lorentz group.
A pure spinor is defined to be any element () that is annihilated by a maximal isotropic subspace with respect to the scalar product . Conversely, given a maximal isotropic subspace it is possible to determine the pure spinor that annihilates it, up to multiplication by a complex number, as follows.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more
In quantum mechanics, the spinor spherical harmonics [1] (also known as spin spherical harmonics, [2] spinor harmonics [3] and Pauli spinors [4]) are special functions defined over the sphere. The spinor spherical harmonics are the natural spinor analog of the vector spherical harmonics .
where ~ is the spin connection, a lifting of the Levi-Civita connection on M to the spinor bundle over M. The square in this case is not the Laplacian, but instead D 2 = Δ + R / 4 {\displaystyle D^{2}=\Delta +R/4} where R {\displaystyle R} is the scalar curvature of the connection.
The corresponding spinor can be taken as any non zero column. Since a 2 + b 2 + c 2 = 1 {\displaystyle a^{2}+b^{2}+c^{2}=1} the different columns are multiples of the same spinor. The representation of the resulting spinor in the Dirac basis can be obtained using the rule given in the bispinor article.
Spinor field, assignment of a spinor to every point in space, used in quantum mechanics and quantum field theory. Spin (physics) the spin property of elementary particles. A kind of Torsion field , used in pseudophysics .