Problems
149
Problems
15.1 Verify equation (15.10).
15.2 Verify equation (15.27).
15.3 Check that (15.50) can be rewritten as (15.53).
15.4 (a) Verify (15.61). (b) Show that the next term in the expansion (15.60)
is
(b 2 − b
2 )
1 α s
β 0
where b 2 = β 2 /β 0 . By iteratively solving the resulting modified equation
(15.60), show that the corresponding correction to (15.61) is
+
1 [b 1
2 (ln
2 L
2
− ln L − 1) + b 2 ].
β 3 L 3
0
15.5 Verify that for the type of behaviour of the β function shown in figure
15.7(b), α
∗ is reached as q
2
→ 0.
s
15.6 Verify equation (15.102).
15.7 Check that the electromagnetic charge e has dimension (mass)
∈/2 in
d = 4 − ∈ dimensions.
15.8 Verify equation (O.20) in appendix O.
15.9 Verify equation (15.118).