254
18. Chiral Symmetry Breaking
where
∂L ˆ
∂(δL ˆ )
ˆ j
αμ (x) = −iT
α ˆ
=
rs φ s
∂(∂ μ φ ˆ r )
∂(∂ μ ∈ α (x)))
and
∂(δL ˆ )
∂ μ ˆ j
αμ (x) =
.
(1)
∂∈ α (x)
Deduce that if L ˆ is invariant under the global form of this transformation (i.e. constant ∈ α ), then the current defined by (1) is conserved.
[This procedure for finding conserved currents for global symmetries
is due to Gell-Mann and Levy (1960).]
(b) Apply the method of part (a) to verify the form of the currents (18.96)
and (18.97).
18.7 Verify equations (18.120)–(18.124).
18.8 Verify (18.132), and calculate the π
0 lifetime in seconds.
18.9 Verify (18.134).
18. Chiral Symmetry Breaking
where
∂L ˆ
∂(δL ˆ )
ˆ j
αμ (x) = −iT
α ˆ
=
rs φ s
∂(∂ μ φ ˆ r )
∂(∂ μ ∈ α (x)))
and
∂(δL ˆ )
∂ μ ˆ j
αμ (x) =
.
(1)
∂∈ α (x)
Deduce that if L ˆ is invariant under the global form of this transformation (i.e. constant ∈ α ), then the current defined by (1) is conserved.
[This procedure for finding conserved currents for global symmetries
is due to Gell-Mann and Levy (1960).]
(b) Apply the method of part (a) to verify the form of the currents (18.96)
and (18.97).
18.7 Verify equations (18.120)–(18.124).
18.8 Verify (18.132), and calculate the π
0 lifetime in seconds.
18.9 Verify (18.134).