## Effective Field TheoriesThis book is a broad-based text intended to help the growing student body interested in constructing and applying methods of effective field theory to solve problems in their research. It begins with a review of using symmetries to identify the relevant degrees of freedom in a problem, and then presents a variety of methods that can be used to construct various effective theories. A detailed discussion of canonical applications of effective field theory techniques with increasing complexity is given, including Fermi's weak interaction, heavy-quark effective theory, and soft-collinear effective theory. Applications of these techniques to study physics beyond the standard model, dark matter, and quantum and classical gravity are explored. Although most examples come from questions in high-energy physics, many of the methods can also be applied in condensed-matter settings. Appendices include various factoids from group theory and other topics that are used throughout the text, in an attempt to make the book self-contained. |

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### Contents

1 Introduction | 1 |

2 Symmetries | 9 |

3 Elementary Techniques | 41 |

4 Effective Field Theories of Type I | 65 |

5 Effective Field Theories of Type II Part A | 107 |

6 Effective Field Theories of TypeII Part B | 145 |

7 Effective Field Theories of TypeIII Fast Particles in Effective Theories | 171 |

8 Standard Model as an Effective Field Theory | 203 |

9 Effective Field Theories of Gravity | 219 |

10 Outlook | 249 |

Appendix A Review of Group Theory | 253 |

Appendix B Short Review of QED and QCD | 269 |

Appendix C Useful Features of Dimensional Regularization | 279 |

291 | |

301 | |

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### Common terms and phrases

action amplitude anomalous appear apply bosons bound calculations called chapter chiral coefficients collinear compute consider constant contains contributions corrections coupling decay defined degrees of freedom dependence derivative described diagrams dimension dimensional discussed divergences effective effective field theory effective theory energy equation example expansion expect fact factor fermion Feynman final function gauge given gives gluon graviton gravity heavy quark HQET important integral interactions introduced invariant Lagrangian leading light limit loop mass matching matrix elements means meson momentum Note Notice obtained operators parameter particles perturbation physics possible potential power counting problem propagator quantum quantum mechanics relation renormalization representation represents require result rules scalar scale SCET scheme simply symmetry theorem transformation usual vector write