Elements of Modern Physics
376
where Q is the charge, B is the baryon number, and I z is the z-component of the
isotopic spin. The combination S + B is called the hypercharge Y and is often
more convenient to use than strangeness. This relation implies that the
conservation of strangeness is equivalent to the conservation of charge and I z . It
needs a slight modification once particles with nonzero charm are included:
Q =
1
2
(S + B + C) + I z
(10.29)
where C is the charm of the particle. The relation will require further modification
if top and bottom quarks are included.
Parity Violation
Weak interaction violates another important conservation low, namely the
conservation of parity.
It had been observed that the laws of nature generally do not appear to
distinguish between a coordinate frame and an inverted coordinate frame, i.e.
the equations of motion are the same whether coordinates (x, y, z) or
(–x, – y, –z) are used. This is termed as invariance under space inversion or
parity transformation. Let us define an operator P called the parity operator,
which takes the wave function ψ(x, y, z) in a coordinate frame, into a wave
function ψ′(x, y, z) observed for the same state but in a coordinate frame with
inverted axes:
ψ′(x, y, z) = Pψ(x, y, z)
(10.29a)
However, ψ′(x, y, z) is essentially the same as ψ(–x, –y, –z) except for a
possible phase factor A, so that
ψ′(x, y, z) = p i ψ(–x, –y, –z)
(10.30)
Now a second operation by P leads us back to the original wave function so
that
ψ(x, y, z) = Pψ′(x, y, z)
= p i
2
ψ(x, y, z)
(10.31)
which implies that
p i = ± 1
(10.32)
The states with p i = 1 are said to be even intrinsic parity states and the states
with p i = –1 are said to be odd intensity parity states. Furthermore, let us assume
that
ψ(–x, –y, –z) = p e ψ(x, y, z)
(10.33)
where p e is called the spatial parity of the state. This relation together to p i , p e
Eqs. (10.30), (10.29) implies
Pψ(x, y, z) = p i p e ψ(x, y, z)
(10.34)
so that there exist eigenstates of parity with eigenvalues equal to p i p e which are
the product of intrinsic parity and spatial parity eigenvalues.
376
where Q is the charge, B is the baryon number, and I z is the z-component of the
isotopic spin. The combination S + B is called the hypercharge Y and is often
more convenient to use than strangeness. This relation implies that the
conservation of strangeness is equivalent to the conservation of charge and I z . It
needs a slight modification once particles with nonzero charm are included:
Q =
1
2
(S + B + C) + I z
(10.29)
where C is the charm of the particle. The relation will require further modification
if top and bottom quarks are included.
Parity Violation
Weak interaction violates another important conservation low, namely the
conservation of parity.
It had been observed that the laws of nature generally do not appear to
distinguish between a coordinate frame and an inverted coordinate frame, i.e.
the equations of motion are the same whether coordinates (x, y, z) or
(–x, – y, –z) are used. This is termed as invariance under space inversion or
parity transformation. Let us define an operator P called the parity operator,
which takes the wave function ψ(x, y, z) in a coordinate frame, into a wave
function ψ′(x, y, z) observed for the same state but in a coordinate frame with
inverted axes:
ψ′(x, y, z) = Pψ(x, y, z)
(10.29a)
However, ψ′(x, y, z) is essentially the same as ψ(–x, –y, –z) except for a
possible phase factor A, so that
ψ′(x, y, z) = p i ψ(–x, –y, –z)
(10.30)
Now a second operation by P leads us back to the original wave function so
that
ψ(x, y, z) = Pψ′(x, y, z)
= p i
2
ψ(x, y, z)
(10.31)
which implies that
p i = ± 1
(10.32)
The states with p i = 1 are said to be even intrinsic parity states and the states
with p i = –1 are said to be odd intensity parity states. Furthermore, let us assume
that
ψ(–x, –y, –z) = p e ψ(x, y, z)
(10.33)
where p e is called the spatial parity of the state. This relation together to p i , p e
Eqs. (10.30), (10.29) implies
Pψ(x, y, z) = p i p e ψ(x, y, z)
(10.34)
so that there exist eigenstates of parity with eigenvalues equal to p i p e which are
the product of intrinsic parity and spatial parity eigenvalues.