Helicity (particle physics)

The helicity (Greek ἕλιξ, helix " Coiling " ) is in particle physics, the component of the spin of a particle that, ie in the direction of movement, points in the direction of its momentum. For the meaning in chemistry see: helicity in chemistry.

Definitions

The helicity is defined as

Where the vector of the spin and the momentum direction indicated.

• For a mass -affected particles with total spin S, the helicity can 2S 1 different eigenvalues ​​assume ( cf. multiplicity ): for integer S: -S ,-S 1, ..., 0, ..., S -1, S
• For half-integer S: -S ,-S 1, ..., -1 / 2, 1 / 2, ..., S -1, S

Sometimes the helicity is also defined as the component of the total angular momentum in the momentum direction:

The two definitions are equivalent because of the orbital angular momentum, the spin angular momentum and total combined, always perpendicular to the momentum vector and, therefore, may not contribute to the dot ().

Descriptive Description

Clearly defines the helicity of the direction of rotation or the handedness of a particle. Looking at the term in the sense of classical mechanics, this means positive helicity that the rotational axis of the particle "forward", that is, is inclined in the direction of movement. The direction of the rotation axis is set so that the rotation of the particle takes place in the direction of the fingers of the right hand when the thumb of the same hand in the proper direction of the axis of rotation. Considered one the path of a point on the surface of such a classical particle, would run this by a " right-handed helix ," as they are known by the thread of a conventional screw. Particles with positive helicity is referred to as right-handed, therefore, those with negative helicity accordingly as left-handed.

However, it should be noted that it is by analogy to illustrate that does not reflect the true quantum-mechanical nature of the particles completely.

Helicity and Relativity

As part of the theory of relativity, the helicity is only for massless particles (which always move at light speed ) uniquely determined. For all involving mass particles, however, always be a frame of reference, select " overtaken " the particle that through which the direction of its momentum and thus reverses its helicity.

Helicity and quantum theory

In quantum physics, one uses the Lorentz - invariant quantity of chirality. The charged currents of the weak interaction (exchange of W - bosons ) are subject only particles with left-handed chirality. For massless particles are chirality and helicity are equivalent and exactly opposite in massless antiparticles. This means that only ( massless ) loaded weakly interacting particles with negative helicity and antiparticles with positive helicity.

As for neutrinos, which are subject only to the weak interaction, experimental long no rest mass could be detected because they only interact weakly with matter, it was assumed that there are only left-handed (negative helicity ) neutrinos and right-handed (positive helicity, but negative chirality ) antineutrinos are. From the discovery of neutrino oscillations but followed that neutrinos must have a non- vanishing rest mass. This means that neutrinos do not move quite the speed of light. It follows on the current physical knowledge that there has to be right-handed neutrinos and left-handed antineutrinos.

Helicity in the chemical

(M) - helicity in chemistry at the example of (M ) - heptahelicene

(P) - helicity in the architecture of a spiral staircase in the Vatican Museum

(M) - helicity of a mirror image of the original spiral staircase in the Vatican Museum

At the molecular level, there are certain materials for which there are isomeric to each other links, such as the helicenes in chemistry. So behave as ( P) heptahelicene and (M) - heptahelicene mirror image. Both molecules have the same number of carbon and hydrogen atoms and are exclusively composed of fused benzene rings, are nonetheless ( P) heptahelicene and (M) - heptahelicene different and can not be made ​​to coincide, they are chiral. This is reflected in the architecture (see illustrations).