Intrinsic parities of fermions and bosons Intrinsic parity can be defined if a particle is at rest For scalars spin 0 vectors spin 1 and tensors parity is equivalent to a rotation by 2π P ID: 540283 Download Presentation
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Slide1
Countries that signed the nuclear arms treaty with Iran Slide2
Intrinsic parities of fermions and bosons
Intrinsic parity can be defined if a particle is at rest.
For scalars (spin 0), vectors (spin 1) and tensors, parity is equivalent to a rotation by 2π
P
2=1 so P= ±1
Subtle point: Bosons have welldefined parity but fermions (spin ½) are spinors and produced in pairs. So one can define relative parity of fermions and antifermions that satisfy the Dirac equation. In addition, the parity of Dirac fermions can be real or imaginary. By convention, we choose it to be real.
p.91
Intrinsic Parities of fermions and antifermions are oppositeSlide3
Intrinsic parities of fermions and bosons (continued)
Question: What is the J
P
for the photon ?
Answer: 1

Question: What is the J
P for a pion (and an antipion) ?Answer: OSlide4
Example of parity of a twobody system with relative orbital angular
momentum l
The derivation closely follows the example that we did for the hydrogen atom last time.
Here P
1
and P
2 are the intrinsic parities of the two particles.
Question: What is the parity of two pions in a pwave (l=1) state ?
Answer: P(pion)P(pion)(1) = 1
Question: What is the parity of a proton and antiproton in an orbital angular momentum state l?
Ans
: These are fermions (spin ½) so they have opposite intrinsic parities. (1)(1)
l
= (1)
l+1Slide5
Question: What are the possible values of J
P
for a spin ½ particle and its antiparticle if they are in a Swave state or a Pwave state (an example in atomic physics is
positronium)
Hint: addition of angular momentum in QM
Do you understand the spectroscopic notation ? What is the left superscript ?Slide6
Charge conjugation (continued)
C eigenvalues of the photon and π
0
Question: What is the charge conjugation of the π
0
?
Ans
: it is the charge conjugation of two photons ? (1)(1) = +1
Question: What does the charge conjugation operator do to a charged pion ?Slide7
Charge conjugation (continued)
Question: What is the charge conjugation of a charged meson
antimeson
pair with relative orbital angular momentum l ? (Do two cases: when the mesons are spin zero and when they have nonzero spin)
Hint: M+ M and M and M+ under C.
Now let’s try spin 1 mesons (spin 0, 1, 2). What is the symmetry of spin 0, 2 ?
So there is an extra factor of (1)
sSlide8
Slide9
Time reversal and CPT
There is a theorem from QFT (Quantum Field Theory) called the CPT theorem, which states if a local theory of interacting fields is invariant under the proper Lorentz group, it will also be invariant under the combination of C (particleanti particle conjugation), space inversion (P) and time reversal (T).
Consequences: if CP is violated then T is violated (and the theory is not invariant under the reversal of the direction of time
particle
AntiparticleSlide10
ASACUSA (low energy antiproton experiment at CERN)
2003Slide11
Mystery of charged pion decay
But the ratio of phase space volume goes like p(electron)/p(
muon
) as discussed in Chapter 1.
Question: How can we the four order of magnitude discrepancy ?
Two body decay kinematicsSlide12
Slide13
Question: But why are
muons
and electrons different ?
Answer: the ratio of the masses 106 MeV (
muon) versus 0.511 MeV (electron)
The VA nature of the weak interaction explains the m
l2
(masssquared) dependence of the decay rate.