## Quantum Field TheoryQuantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497. |

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### Contents

3 | |

8 | |

Scattering amplitudes and the Feynman rules 5 9 | 73 |

Cross sections and decay rates 10 | 79 |

Dimensional analysis with h c 1 3 | 90 |

The LehmannKallen form of the exact propagator 9 | 93 |

Loop corrections to the propagator 10 12 13 | 96 |

The oneloop correction in LehmannKallen form 14 | 107 |

Spin One | 333 |

Maxwells equations 3 | 335 |

Electrodynamics in Coulomb gauge 54 | 339 |

LSZ reduction for photons 5 55 | 344 |

The path integral for photons 8 56 | 349 |

Spinor electrodynamics 45 57 | 351 |

Scattering in spinor electrodynamics 48 58 | 357 |

Spinor helicity for spinor electrodynamics 50 59 | 362 |

Loop corrections to the vertex 14 | 111 |

Other 1PI vertices 16 | 115 |

Higherorder corrections and renormalizability 17 | 117 |

Perturbation theory to all orders 18 | 121 |

Twoparticle elastic scattering at one loop 19 | 123 |

The quantum action 19 | 127 |

Continuous symmetries and conserved currents 8 | 132 |

P T C and Z 22 | 140 |

Nonabelian symmetries 22 | 146 |

Unstable particles and resonances 14 | 150 |

Infrared divergences 20 | 157 |

Other renormalization schemes 26 | 162 |

The renormalization group 27 | 169 |

Eﬀective ﬁeld theory 28 | 176 |

Spontaneous symmetry breaking 21 | 188 |

Broken symmetry and loop corrections 30 | 192 |

Spontaneous breaking of continuous symmetries 22 30 | 198 |

Spin One Half | 203 |

Representations of the Lorentz group 2 | 205 |

Left and righthanded spinor ﬁelds 3 33 | 209 |

Manipulating spinor indices 34 | 216 |

Lagrangians for spinor ﬁelds 22 35 | 221 |

Canonical quantization of spinor ﬁelds I 36 | 232 |

Spinor technology 37 | 237 |

Canonical quantization of spinor ﬁelds II 38 | 244 |

Parity time reversal and charge conjugation 23 39 | 252 |

LSZ reduction for spinonehalf particles 5 39 | 261 |

The free fermion propagator 39 | 267 |

The path integral for fermion ﬁelds 9 42 | 271 |

Formal development of fermionic path integrals 43 | 275 |

The Feynman rules for Dirac ﬁelds 10 12 41 43 | 282 |

Spin sums 45 | 291 |

Gamma matrix technology 36 | 294 |

Spinaveraged cross sections 46 47 | 298 |

The Feynman rules for Majorana ﬁelds 45 | 303 |

Massless particles and spinor helicity 48 | 308 |

Loop corrections in Yukawa theory 19 40 48 | 314 |

Beta functions in Yukawa theory 28 51 | 324 |

Functional determinants 44 45 | 327 |

Scalar electrodynamics 58 | 371 |

Loop corrections in spinor electrodynamics 51 59 | 376 |

The vertex function in spinor electrodynamics 62 | 385 |

The magnetic moment of the electron 63 | 390 |

Loop corrections in scalar electrodynamics 61 62 | 394 |

Beta functions in quantum electrodynamics 52 62 | 403 |

Ward identities in quantum electrodynamics I 22 59 | 408 |

Ward identities in quantum electrodynamics II 63 67 | 412 |

Nonabelian gauge theory 24 58 | 416 |

Group representations 69 | 421 |

The path integral for nonabelian gauge theory 53 69 | 430 |

The Feynman rules for nonabelian gauge theory 71 | 435 |

The beta function in nonabelian gauge theory 70 72 | 439 |

BRST symmetry 70 71 | 448 |

Chiral gauge theories and anomalies 70 72 | 456 |

Anomalies in global symmetries 75 | 468 |

Anomalies and the path integral for fermions 76 | 472 |

Background ﬁeld gauge 73 | 478 |

GervaisNeveu gauge 78 | 486 |

The Feynman rules for N N matrix ﬁelds 10 | 489 |

Scattering in quantum chromodynamics 60 79 80 | 495 |

Wilson loops lattice theory and conﬁnement 29 73 | 507 |

Chiral symmetry breaking 76 82 | 516 |

Spontaneous breaking of gauge symmetries 32 70 | 526 |

Spontaneously broken abelian gauge theory 61 84 | 531 |

Spontaneously broken nonabelian gauge theory 85 | 538 |

gauge and Higgs sector 84 | 543 |

lepton sector 75 87 | 548 |

quark sector 88 | 556 |

Electroweak interactions of hadrons 83 89 | 562 |

Neutrino masses 89 | 572 |

Solitons and monopoles 84 | 576 |

Instantons and theta vacua 92 | 590 |

Quarks and theta vacua 77 83 93 | 601 |

Supersymmetry 69 | 610 |

The Minimal Supersymmetric Standard Model 89 95 | 622 |

Grand uniﬁcation 89 | 625 |

637 | |

### Common terms and phrases

anticommutation antisymmetric beta function boson charge chiral coeﬃcients complex scalar compute consider corrections corresponding counterterm coupling covariant derivative cutoﬀ decay deﬁne diﬀerent Dirac field divergent eﬀective electron energy equation evaluate external lines Feynman diagrams Feynman rules ﬁeld ﬁnd ﬁnite ﬁrst four-momentum gauge ﬁeld gauge fields gauge group gauge invariant gauge theory gauge transformation gluon hamiltonian helicity hermitian conjugate identity infinitesimal interaction kinetic term lagrangian left-handed Weyl lepton loop massless matrix minus sign momenta momentum neutrino nonabelian nonzero obey operator parameter parity path integral photon pion Prerequisite problem propagator quantum action quantum ﬁeld theory quark real scalar field renormalization representation result right-hand side scalar field scattering amplitude side of eq space-time spin spinor spinor electrodynamics SU(N supersymmetry symmetry factor tree-level unitary vacuum vanishes vector vertex factor vertex function winding number write Yukawa zero

### Popular passages

Page 9 - Dirac therefore predicted (in 1927) the existence of the positron, a particle with the same mass as the electron, but opposite charge.

Page 3 - The axiom we need to focus on is the one that says that the time evolution of the state of the system is governed by the Schrodinger equation, r\ ,), (ii) where H is the hamiltonian operator, representing the total energy.