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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 ...
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. [a]
Helicity (particle physics), the projection of the spin onto the direction of momentum Magnetic helicity , the extent to which a magnetic field "wraps around itself" Circular dichroism , the differential absorption of left and right circularly polarized light
Helicity is a pseudo-scalar quantity: it changes sign under change from a right-handed to a left-handed frame of reference; it can be considered as a measure of the handedness (or chirality) of the flow. Helicity is one of the four known integral invariants of the Euler equations; the other three are energy, momentum and angular momentum.
Magnetic helicity is a gauge-dependent quantity, because can be redefined by adding a gradient to it (gauge choosing).However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity contained in the whole domain is gauge invariant, [15] that is, independent of the gauge choice.
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Note the freedom one has to equate negative helicity with negative energy, and thus the anti-particle with the particle of opposite helicity. To be clear, the σ {\displaystyle \sigma } here are the Pauli matrices , and p μ = i ∂ μ {\displaystyle p_{\mu }=i\partial _{\mu }} is the momentum operator.
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