## Quantum Field Theory: From Operators to Path IntegralsA new, updated and enhanced edition of the classic work, which was welcomed for its general approach and self-sustaining organization of the chapters. Written by a highly respected textbook writer and researcher, this book has a more general scope and adopts a more practical approach than other books. It includes applications of condensed matter physics, first developing traditional concepts, including Feynman graphs, before moving on to such key topics as functional integrals, statistical mechanics and Wilson's renormalization group. The author takes care to explain the connection between the latter and conventional perturbative renormalization. Due to the rapid advance and increase in importance of low dimensional systems, this second edition fills a gap in the market with its added discussions of low dimensional systems, including one-dimensional conductors. All the chapters have been revised, while more clarifying explanations and problems have been added. A FREE SOLUTIONS MANUAL is available for lecturers from www.wiley-vch.de/textbooks. |

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### Contents

Scalar Fields | 17 |

Relativistic Fields | 39 |

Canonical Formalism | 55 |

Electromagnetic Field | 69 |

Dirac Equation | 95 |

The Dirac Field | 123 |

Dynamics of Interacting Fields | 139 |

Feynman Graphs | 159 |

Path Integrals | 261 |

Broken Symmetry | 291 |

Renormalization | 315 |

The Gaussian Fixed Point | 339 |

In two Dimensions | 357 |

Topological Excitations | 375 |

Appendix A Background Material | 399 |

Appendix B Superfluidity | 405 |

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### Common terms and phrases

4-momentum amplitude annihilation operators antiparticle boson boundary conditions calculate charge classical components conjugate conservation Consider coordinate correlation function corresponds Coulomb gauge coupling constant cutoff defined denoted Dirac equation divergent eigenstate eigenvalue electromagnetic field energy equation of motion Euclidean external lines factor fermion Feynman graphs field operator finite Gaussian fixed point given Hamiltonian Hopf invariant interaction Lagrangian density limit linear loop Lorentz boost Lorentz transformation magnetic mass matrix element momenta non-relativistic normalization obtain one-particle Operators to Path parameter particle partition function Path Integrals perturbation phase photon Phys physical polarization potential Problem propagator quantized Quantum Field Theory renormalization replace representation rewrite rotation S-matrix scalar field scale scattering self-energy Skyrmion soliton solution space space-time spatial spin spinor superfluid symmetry tensor term theorem Theory from Operators tion topological trajectory vacuum graphs variables vector velocity vertex vortices wave function write zero