## A First Book of Quantum Field TheoryThis book introduces QFT for readers with no prior knowledge of the subject. It is meant to be a textbook for advanced undergraduate or beginning postgraduate students. The book discusses quantization of fields, S-matrix theory, Feynman diagrams, calculation of decay rates and cross sections, renormalization, symmetries and symmetry breaking. Some background material on classical field theory and group theory, needed for the exposition, are also presented in the book. Detailed calculations of weak and electromagnetic processes are included. There are many exercise problems to help the students, instructors and beginning researchers in the field. The second edition improves upon some notations and explanations, and includes answers to selected exercises. |

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### Contents

Preliminaries | 1 |

Classical Field Theory | 12 |

Quantization of scalar fields | 28 |

Quantization of Dirac fields | 47 |

The Smatrix expansion | 72 |

From Wick expansion to Feynman diagrams | 87 |

Cross sections and decay rates | 115 |

Quantization of the electromagnetic field | 146 |

P T C and their combinations | 200 |

Electromagnetic form factors | 222 |

Renormalization | 245 |

Symmetries and symmetry breaking | 283 |

YangMills theory of nonAbelian gauge fields | 312 |

Standard electroweak theory | 326 |

Traces of matrices | 360 |

B Answers to selected exercises | 368 |

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### Common terms and phrases

7-matrices annihilation operators anticommutation antiparticle calculate called charge conjugation classical co-ordinates commutation relation components conserved consider contribution counterterm coupling constant covariant cross section cross-section decay rate defined in Eq denote derivative Dirac equation discussed eigenstates electron energy example Exercise expression external fermion fields fermion lines Feynman amplitude Feynman diagram Feynman rule field theory final form factor Fourier free Lagrangian function gauge boson gauge fields gauge theory given in Eq Hamiltonian hermitian initial integration interaction term internal lines involving J-function Lagrangian Lagrangian of Eq leptons loop Lorentz invariant Lorentz transformation lowest order massless matrix element momenta momentum muon neutrino obtain on-shell parameters parity particles photon photon field physical polarization vectors propagator quantity quantization quantum field quarks representation S-matrix satisfy scalar field Shoui Show space-time point spin spinors symmetry breaking tensor theorem trace vacuum polarization vanishes variables vertex vertex function write written zero