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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 restricted Lorentz group is a connected normal subgroup of the full Lorentz group with the same dimension, in this case with dimension six. The restricted Lorentz group is generated by ordinary spatial rotations and Lorentz boosts (which are rotations in a hyperbolic space that includes a time-like direction [2]).
If a representation Π of a Lie group G is not faithful, then N = ker Π is a nontrivial normal subgroup. [89] There are three relevant cases. N is non-discrete and abelian. N is non-discrete and non-abelian. N is discrete. In this case N ⊂ Z, where Z is the center of G. [nb 24] In the case of SO(3; 1) +, the first case is excluded since SO(3 ...
An experiment to test the theory of relativity cannot assume the theory is true, and therefore needs some other framework of assumptions that are wider than those of relativity. For example, a test theory may have a different postulate about light concerning one-way speed of light vs. two-way speed of light, it may have a preferred frame of ...
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]
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 ...
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.
In electromagnetism, the Lorenz gauge condition or Lorenz gauge (after Ludvig Lorenz) is a partial gauge fixing of the electromagnetic vector potential by requiring = The name is frequently confused with Hendrik Lorentz, who has given his name to many concepts in this field. [1]