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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.
[nb 1] This group is significant because special relativity together with quantum mechanics are the two physical theories that are most thoroughly established, [nb 2] and the conjunction of these two theories is the study of the infinite-dimensional unitary representations of the Lorentz group. These have both historical importance in ...
Since the helicity of massive particles is frame-dependent, it might seem that the same particle would interact with the weak force according to one frame of reference, but not another. The resolution to this paradox is that the chirality operator is equivalent to helicity for massless fields only, for which helicity is not frame-dependent. By ...
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.
Painting of Hendrik Lorentz by Menso Kamerlingh Onnes, 1916 Portrait by Jan Veth Lorentz' theory of electrons. Formulas for the Lorentz force (I) and the Maxwell equations for the divergence of the electrical field E (II) and the magnetic field B (III), La théorie electromagnétique de Maxwell et son application aux corps mouvants, 1892, p. 451.
In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also ...