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Note that the only possible eigenvalues of the operation of a discrete symmetry are +1 and −1.
Warning, this drawing
contains a common error. There are two kinds of
vectors, and vector operators: polar and axial.
Parity changes the sign of polar vectors, but not of
axial vectors! |
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Warning, this drawing might contain a common error.
 Combined C and P Warning, this drawing contains a common error. |
 Helicity--- h = 2S·p/(ℏp). |
Intrinsic parity is something I usually have to look up in a table. However, some usages are obvious. For example, a "pseudoscalar" particle is one which has spin zero, but negative parity. [We would normally associate scalars with positive parity!] Hence, a 0− particle is called a pseudoscalar particle.
It was realized in 1957 that weak interactions are not P-symmetric, but PC was still thought to be a good symmetry. However, in 1964 it was found that neutral K (497.6 MeV) decays violate CP conservation. [See H & G, 9.6, 9.7, 9.8] However, this is so-called “indirect CP violation.” The observed K mesons are oscillating mixtures of the particle and antiparticle (CP eigenvalues -1 and +1) so that both -1 and +1 decays can be seen from the “same” particle. What physicists needed to see desperately was “direct CP violation,” in which a pure -1 state decays directly into a +1 state. Such decays are less than 1 in 106 and were seen for neutral kaons only in 1999. They were then seen for neutral B mesons (5.279 GeV) in 2001 and for neutral D mesons (1.864 GeV) in 2011.
Particle-antiparticle mixing diagram. |
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In the earliest moments of the universe, antiparticles MUST have behaved differently than particles to some extent, in order to produce an excess of particles after the mutual annihlation of particle-antiparticle pairs produced by decay of unknown heavy bosons or other obscure processes. For every billion antiparticles, there must have been a billion plus one particles.
The incredible sensitivity of these experiments to the mass difference, found to astonishing precision!
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Explicit representation of a discrete symmetry operator can be very difficult. Even simple discrete symmetries give much food for thought. For example, the time-reversal operator has to be anti-unitary! The problem is that for fundamental processes, the time reversal operator should commute with the Hamiltonian. But the Hamiltonian operator in time representation is iℏ(∂/∂t). So the time reversal operator will not commute with the Hamiltonian unless it complex conjugates as well as changes t to −t.
