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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 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.
Helicity may refer to: Helicity (fluid mechanics), the extent to which corkscrew-like motion occurs; 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"
This glossary of physics is a list of definitions of terms and concepts relevant to physics, its sub-disciplines, and related fields, including mechanics, materials science, nuclear physics, particle physics, and thermodynamics.
Helicity is the projection (dot product) of a spin pseudovector onto the direction of momentum (a true vector). Pseudoscalar particles, i.e. particles with spin 0 and odd parity, that is, a particle with no intrinsic spin with wave function that changes sign under parity inversion. Examples are pseudoscalar mesons.
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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.