Quantum Field TheoryThis book is a modern introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the author develops the quantum theory of scalar and spinor fields, and then of gauge fields. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of "topological" objects in field theory and, new to this edition, a chapter devoted to supersymmetry. Graduate students in particle physics and high energy physics will benefit from this book. 
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This textbook is probably one of the most readable books on Quantum Field Theory. The level of formalism and mathematical complexity varies from chapter to chapter, which has its virtues and drawbacks. The chapters that are not too mathheavy are usually the more intelligible ones, and they present the otherwise fairly arcane material in a very accessible and physicallymotivated fashion. On the other hand these chapters leave out a lot of calculation or just skim through those somewhat superficially. If you are trying to learn Quantum Field Theory so that you become proficient enough to pursue research in this field, then you may find this lack of detail frustrating.
One of the virtues of this book are the extended references that can be found at the ends of chapters. These refer both to the original research papers and other books that may cover the same material in more depth or with a different approach. These references are invaluable in their own right, and make this book a great resource to have.
The last chapter focuses on supersymmetry. This could be viewed as a somewhat controversial choice of topic to be included in a textbook that covers the fundamentals of quantum field theory. Supersymmetry, despite decades of theoretical investigation, so far has not yielded a single observable verification. There might be something in the claims of its proponents that it has a very appealing conceptual and mathematical structure, but even its simplest formulation that have any bearing on the real world are so complex that any traces of conceptual simplicity are irrevocably lost. However, whatever your feelings about supersymmetry might be, this chapter is valuable in its own right, since it gives a lot of interesting mathematics that are relevant to fermionic and bosonic fields in general.
One big problem that I have with this book as a textbook is a total lack of problems and exercises. As such is probably not well suited as a primary book for learning this material. Nonetheless, there are some detailed calculations of some important formal results, and these can be used in conjunction with other textbooks.
I would recommend this book to be used as a secondary study material for an introductory course on Quantum Field Theory. This way all of its strong points would be utilized, while its few weaknesses would not be an obstacle to fully absorbing otherwise very difficult material.
Contents
Introduction synopsis of particle physics  1 
12 Gravitation  2 
13 Strong interactions  3 
14 Weak interactions  4 
15 Leptonic quantum numbers  5 
16 Hadronic quantum numbers  7 
17 Resonances  8 
18 The quark model  9 
72 NonAbelian gauge fields and the FaddeevPopov method  245 
Feynman rules in the Lorentz gauge  250 
Gaugefield propagator in the axial gauge  254 
73 Selfenergy operator and vertex function  255 
Geometrical interpretation of the Legendre transformation  260 
Thermodynamic analogy  262 
74 WardTakahashi identities in QED  263 
75 BecchiRouetStora transformation  270 
19 SU2 SU3 SU4 The particles A Fig 13 have the quark content  12 
110 Dynamical evidence for quarks  15 
111 Colour  18 
112 QCD  22 
113 Weak interactions  23 
Guide to further reading  24 
Singleparticle relativistic wave equations 21 Relativistic notation  25 
22 KleinGordon equation  27 
23 Dirac equation  29 
Su2 and the rotation group  30 
St2 C and the Lorentz group  36 
24 Prediction of antiparticles  42 
algebra of y matrices  46 
26 Nonrelativistic limit and the electron magnetic moment  52 
spin operators and the zero mass limit  55 
28 Maxwell and Proca equations  64 
29 Maxwells equations and differential geometry  69 
Summary  77 
Lagrangian formulation symmetries and gauge fields  79 
31 Lagrangian formulation of particle mechanics  80 
variational principle and Noethers theorem  81 
33 Complex scalar fields and the electromagnetic field  90 
the BohmAharonov effect  98 
35 The YangMills field  105 
36 The geometry of gauge fields  112 
Summary  124 
Guide to further reading  125 
Canonical quantisation and particle interpretation  126 
42 The complex Klein Gordon field  135 
43 The Dirac field  137 
44 The electromagnetic field  140 
Radiation gauge quantisation  142 
Lorentz gauge quantisation  145 
45 The massive vector field  150 
Summary  152 
Guide to further reading  153 
Path integrals and quantum mechanics  154 
52 Perturbation theory and the S matrix  161 
53 Coulomb scattering  170 
differentiation  172 
55 Further properties of path integrals We have shown that the transition amplitude from qt to qttf is given by  174 
some useful integrals  179 
Summary  181 
Pathintegral quantisation and Feynman rules scalar and spinor fields  182 
62 Functional integration  186 
63 Free particle Greens functions  189 
64 Generating functionals for interacting fields  196 
65 04 theory  200 
2point function  202 
4point function  204 
66 Generating functional for connected diagrams  207 
67 Fermions and functional methods  210 
68 The S matrix and reduction formula  217 
69 Pionnucleon scattering amplitude  224 
610 Scattering cross section  232 
Summary  238 
Guide to further reading  239 
Pathintegral quantisation gauge fields  240 
Photon propagator pathintegral method Here we simply consider the generating functional  242 
Propagator for transverse photons  243 
76 SlavnovTaylor identities  273 
77 A note on ghosts and unitarity  276 
Summary  280 
Guide to further reading  281 
Spontaneous symmetry breaking and the WeinbergSalam model  282 
82 The Goldstone theorem  287 
83 Spontaneous breaking of gauge symmetries  293 
84 Superconductivity  296 
85 The WeinbergSalam model  298 
Summary  306 
Guide to further reading  307 
Renormalisation  308 
Dimensional analysis  311 
92 Dimensional regularisation of theory  313 
Loop expansion  317 
93 Renormalisation of if theory  318 
Counterterms  321 
94 Renormalisation group  324 
95 Divergences and dimensional regularisation of QED  329 
96 1loop renormalisation of QED  337 
Anomalous magnetic moment of the electron  343 
Asymptotic behaviour  345 
97 Renormalisability of QED  347 
98 Asymptotic freedom of YangMills theories  353 
99 Renormalisation of pure YangMills theories  362 
910 Chiral anomalies  366 
Cancellation of anomalies  373 
breakdown  375 
The effective potential  377 
Loop expansion of the effective potential  380 
integration in d dimensions  382 
the gamma function  385 
Summary  387 
Guide to further reading  388 
10 Topological objects in field theory  390 
101 The sineGordon kink  391 
102 Vortex lines  395 
103 The Dirac monopole  402 
104 The i HooftPolyakov monopole  406 
105 Instantons  414 
Quantum tunnelling 0vacua and symmetry breaking  420 
Summary  424 
Supersymmetry  426 
112 Lorentz transformations Dirac Weyl and Majorana spinors  427 
Some further relations  436 
113 Simple Lagrangian model  440 
Fierz rearrangement formula  444 
closure of commutation relations  446 
Mass term  450 
115 Towards a superPoincare algebra  452 
116 Superspace  459 
117 Superfields  464 
Chiral superfield  467 
118 Recovery of the WessZumino model  470 
some 2spinor conventions  473 
Summary  475 
476  
482  