Contents
Preface
xiii
V Non-Abelian Symmetries
1
12 Global Non-Abelian Symmetries
3
12.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . .
3
12.2 The flavour symmetry SU(2) f . . . . . . . . . . . . . . . . . .
5
12.2.1 The nucleon isospin doublet and the group SU(2) . . .
5

12.2.2 Larger (higher-dimensional) multiplets of SU(2) in nuclear physics . . . . . . . . . . . . . . . . . . . . . . .
12
12.2.3 Isospin in particle physics: flavour SU(2) f . . . . . . .
14
12.3 Flavour SU(3) f . . . . . . . . . . . . . . . . . . . . . . . . . .
18
12.4 Non-Abelian global symmetries in Lagrangian quantum field

theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
12.4.1 SU(2) f and SU(3) f . . . . . . . . . . . . . . . . . . . .
24
12.4.2 Chiral symmetry . . . . . . . . . . . . . . . . . . . . .
31
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
13 Local Non-Abelian (Gauge) Symmetries
39
13.1 Local SU(2) symmetry . . . . . . . . . . . . . . . . . . . . .
40
13.1.1 The covariant derivative and interactions with matter
40

13.1.2 The non-Abelian field strength tensor . . . . . . . . .
48
13.2 Local SU(3) Symmetry . . . . . . . . . . . . . . . . . . . . .
49
13.3 Local non-Abelian symmetries in Lagrangian quantum field

theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
13.3.1 Local SU(2) and SU(3) Lagrangians . . . . . . . . . .
51

13.3.2 Gauge field self-interactions . . . . . . . . . . . . . .
54

13.3.3 Quantizing non-Abelian gauge fields . . . . . . . . . .
60

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
VI QCD and the Renormalization Group
71
14 QCD I: Introduction, Tree Graph Predictions, and Jets
73
14.1 The colour degree of freedom . . . . . . . . . . . . . . . . . .
74
14.2 The dynamics of colour . . . . . . . . . . . . . . . . . . . . .
78
14.2.1 Colour as an SU(3) group . . . . . . . . . . . . . . . .
78

14.2.2 Global SU(3) c invariance, and ‘scalar gluons’ . . . . .
80

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