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The helicity of a particle is positive (" right-handed") if the direction of its spin is the same as the direction of its motion and negative ("left-handed") if opposite. Helicity is conserved. [1] That is, the helicity commutes with the Hamiltonian, and thus, in the absence of external forces, is time-invariant. It is also rotationally ...
The derivative operators, and hence the energy and 3-momentum operators, are also non-invariant and change under Lorentz transformations. Under a proper orthochronous Lorentz transformation (r, t) → Λ(r, t) in Minkowski space, all one-particle quantum states ψ σ locally transform under some representation D of the Lorentz group: [13] [14]
The Lorentz group is a subgroup of the Poincaré group—the group of all isometries of Minkowski spacetime. Lorentz transformations are, precisely, isometries that leave the origin fixed. Thus, the Lorentz group is the isotropy subgroup with respect to the origin of the isometry group of Minkowski spacetime.
E.P. Wigner investigated the Lorentz group in depth and is known for the Bargmann-Wigner equations. The realization of the covering group given here is from his 1939 paper. Let p g (t), 0 ≤ t ≤ 1 be a path from 1 ∈ SO(3; 1) + to g ∈ SO(3; 1) +, denote its homotopy class by [p g] and let π g be the set of all such homotopy classes ...
In theoretical particle physics, maximally helicity violating amplitudes (MHV) are amplitudes with massless external gauge bosons, where gauge bosons have a particular helicity and the other two have the opposite helicity. These amplitudes are called MHV amplitudes, because at tree level, they violate helicity conservation to the maximum extent ...
So, the Weinberg–Witten theorem applies and we can't get a massless spin-2 (i.e. helicity ±2) composite/emergent graviton. If we have a theory with a fundamental conserved 4-current associated with a global symmetry , then we can't have emergent/composite massless spin-1 particles which are charged under that global symmetry.
In addition to being invariant, it is also a kinematic observable, i.e. free of interactions. It is called a helicity because the spin quantization axis is determined by the orientation of the light front. It differs from the Jacob–Wick helicity, where the quantization axis is determined by the direction of the momentum.
Because of this, the direction of spin of massless particles is not affected by a change of inertial reference frame (a Lorentz boost) in the direction of motion of the particle, and the sign of the projection (helicity) is fixed for all reference frames: The helicity of massless particles is a relativistic invariant (a quantity whose value is ...