Preliminary¶
This chapter is about the preliminary knowledge required by this topic.
What is a Neutrino Particle?¶
As Wigner said, a physical particle is an irreducible representation of the Poincaré group. A characteristic of Poincaré group is that mass comes in.
A neutrino particle is better recognized as its mass eigenstate.
In QFT, there are 3 different forms of neutrino mass term, left-handed Majorana, right-handed Majorana and Dirac mass terms.
Chirality and Helicity¶
Helicity¶
Helicity is the projection of spin onto direction of momentum,
where
A state is called right-handed if helicity is positive, i.e., spin has the same direction as momentum.
States¶
Wigner Function¶
Wigner function is an analogue of the classical phase-space probability distribution function though it is not really probability. [3] The mean of Wigner function lies in the two quadratures, i.e., space distribution and momentum distribution.
There is a collection of Wigner functions on this site. [3]
[3] | (1, 2) http://www.iqst.ca/quantech/wigner.php |
- .. admonition:: Question
class: warning How do one describe a system of neutrinos using Wigner function? What is the effect of statistics.