## 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 math-heavy are usually the more intelligible ones, and they present the otherwise fairly arcane material in a very accessible and physically-motivated 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 | |