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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 spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry.
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.
In particular for a massless particle the helicity is the same as the chirality while for an antiparticle they have opposite sign. The handedness in both chirality and helicity relate to the rotation of a particle while it proceeds in linear motion with reference to the human hands. The thumb of the hand points towards the direction of linear ...
where p is the momentum operator, S the spin operator for a particle of spin s, E is the total energy of the particle, and m 0 its rest mass. Helicity indicates the orientations of the spin and translational momentum vectors. [29] Helicity is frame-dependent because of the 3-momentum in the definition, and is quantized due to spin quantization ...
The field equations of condensed matter physics are remarkably similar to those of high energy particle physics. As a result, much of the theory of particle physics applies to condensed matter physics as well; in particular, there are a selection of field excitations, called quasi-particles, that can be created and explored. These include:
In the Standard Model, using quantum field theory it is conventional to use the helicity basis to simplify calculations (of cross sections, for example). In this basis, the spin is quantized along the axis in the direction of motion of the particle.
The first parity transformation given does not work in an even number of dimensions, though, because it results in a positive determinant. In even dimensions only the latter example of a parity transformation (or any reflection of an odd number of coordinates) can be used.