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The conventional definition of the spin quantum number is s = n / 2 , where n can be any non-negative integer. Hence the allowed values of s are 0, 1 / 2 , 1, 3 / 2 , 2, etc. The value of s for an elementary particle depends only on the type of particle and cannot be altered in any known way (in contrast to the spin ...
The spin representation Δ is a vector space equipped with a representation of the spin group that does not factor through a representation of the (special) orthogonal group. The vertical arrows depict a short exact sequence.
Mathematically, helicity is the sign of the projection of the spin vector onto the momentum vector: "left" is negative, "right" is positive. The chirality of a particle is more abstract: It is determined by whether the particle transforms in a right- or left-handed representation of the Poincaré group .
The (total) spin quantum number has only one value for every elementary particle. Some introductory chemistry textbooks describe m s as the spin quantum number, [6] [7] and s is not mentioned since its value 1 / 2 is a fixed property of the electron; some even use the variable s in place of m s. [5]
In physics, chirality may be found in the spin of a particle, where the handedness of the object is determined by the direction in which the particle spins. [4] Not to be confused with helicity , which is the projection of the spin along the linear momentum of a subatomic particle, chirality is an intrinsic quantum mechanical property, like spin.
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.
The general expression for the spin angular momentum is [1] =, where is the speed of light in free space and is the conjugate canonical momentum of the vector potential.The general expression for the orbital angular momentum of light is =, where = {,,,} denotes four indices of the spacetime and Einstein's summation convention has been applied.
Spin- 1 / 2 particles can have a permanent magnetic moment along the direction of their spin, and this magnetic moment gives rise to electromagnetic interactions that depend on the spin. One such effect that was important in the discovery of spin is the Zeeman effect , the splitting of a spectral line into several components in the ...