## Concepts in Quantum Field Theory: A Practitioner's ToolkitThis book uses less strict yet still formal mathematical language to clarify a variety of concepts in Quantum Field Theory that remain somewhat “fuzzy” in many books designed for undergraduates and fresh graduates. The aim is not to replace formal books on Quantum Field Theory, but rather to offer a helpful complementary tool for beginners in the field. Features include a reader-friendly introduction to tensor calculus and the concept of manifolds; a simple and robust treatment for dimensional regularization; a consistent explanation of the renormalization procedure, step by step and in a transparent manner at all orders, using the QED Lagrangian; and extensive treatment of infrared as well as ultraviolet divergences. The most general (Lorentz invariant) form of Noether's theorem is presented and applied to a few simple yet relevant examples in Quantum Field Theory. These and further interesting topics are addressed in a way that will be accessible for the target readership. Some familiarity with basic notions of Quantum Field Theory and the basics of Special Relativity is assumed. |

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### Contents

1 | |

2 Lagrangians Hamiltonians and Noethers Theorem | 28 |

3 Relativistic Kinematics and Phase Space | 47 |

4 Angular Distributions | 57 |

5 Dirac Algebra | 68 |

6 Dimensional Regularization Ultraviolet and Infrared Divergences | 85 |

7 QED Renormalization | 95 |

8 OneLoop Two and ThreePoint Functions | 112 |

9 Massive Spin One and Renormalizable Gauges | 141 |

10 Symmetries and Effective Vertices | 157 |

11 Effective Field Theory | 162 |

12 Optical Theorem | 173 |

Appendix A
Master Integral | 179 |

Appendix B
Renormalization Group Equations | 183 |

Appendix C
Feynman Rules for Derivative Couplings | 188 |