Kinetic momenta and symmetries.

The kinetic moments, in classical mechanics, have many applications: gyroscope, bicycle, nutation of  stars … We use them here in atomic physics, by describing the ancient planetary model of the hydrogen atom, where the electron revolves around the proton, its centrifugal force balancing the electromagnetic attraction force. This model is now abandoned, but it shows that  the concept of kinetic momentum is useful  in atomic physics.

In quantum mechanics, this concept plays an even more important role, though completely different. The « wave functions », which govern the probabilities of presence for all the points of space defined by  polar and azimutal coordinates , depend of kinetic moments, and the values ​​of these are proportional to integers or half-integers. First, we illustrate these wave functions in polar coordinates and more specifically the effects of the Parity operation, which consists of comparing the wave function at a point and the point opposite to it in space (at « antipodes » for a planet).

As certain kinetic moments are, for isolated systems, « constants of the movement » (they do not vary with time whatever the interactions), we understand then that they play a preponderant role in the disintegration of  elementary particles: we thus arrive at selection rules, linked to the rules of symmetry of the interactions producing these decays, strong, electromagnetic, or weak interactions; for the first two, the Parity is conserved;  for the neutral initial states (zero charge and strangeness), the conjugation of Charge C (particle-anti-particle symmetry, or positive charge-negative charge) is also conserved; for strong interactions, the « Parity G », or isotopic independence, is preserved. It is these relations between P, C and G as a function of the kinetic moments which are illustrated for the decays of the « light » mesons, comprising only two of the three lightest quarks.