## Quantum Field Theory Of Point Particles And StringsThe purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.Part II emphasizes the quantization of the bosonic string. The treatment is most detailed in the path integral representation where the object of interest, the partition function, is a sum over random surfaces. The relevant mathematics of Riemann surfaces is covered. Superstrings are briefly introduced, and the sum over genus 0 supersurfaces is computed.The emphasis of the book is calculational, and most computations are presented in step-by-step detail. The book is unique in that it develops all three representations of quantum field theory (operator, functional Schrödinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory. |

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### Contents

3 | |

9 | |

35 | |

Free Spinor Field Theory | 59 |

Quantization of the Electromagnetic Field | 77 |

Interacting Field Theories | 93 |

SelfInteracting Scalar Field Theory | 111 |

Spinor Quantum Electrodynamics | 155 |

YangMills and FaddeevPopov | 341 |

Hiding the Infinities | 361 |

Renormalization of QED at 1Loop | 377 |

The Effective Action | 431 |

Basic Ideas and Classical Theory | 475 |

First Quantization | 503 |

The Mathematics of Surfaces | 535 |

HigherGenus Integrals | 631 |

Functional Calculus | 179 |

Free Fields in the Schrödinger Representation | 199 |

Interacting Fields in the Schrödinger | 225 |

Path Integral Representation | 271 |

Path Integrals in Free Field Theory | 301 |

Interacting Fields and Path Integrals | 329 |

Scattering Amplitudes | 653 |

Noncritical Dimensions | 669 |

Introduction to Superstrings | 687 |

721 | |

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### Common terms and phrases

2-point function 6-function action amplitude anticommuting bosonic chapter charge chiral classical components compute conformal constraint coordinate Coulomb gauge counterterm covariant curvature curve defined derivative determinant diagram diffeomorphism dimension Dirac divergent dºk eigenvalue electron equation of motion equivalent expansion factor Faddeev–Popov fermions figure finite free field gauge invariant gauge slice gauge transformation Gaussian genus Green's function Hamiltonian hence holomorphic homeomorphic identical interacting loop Lorentz invariant mass matrix metric momentum negative energy normal ordering operator path integral perturbative photon propagator physical point particle potential quantization quantum field theory quarks renormalized represents result Riemann surfaces ſ dºr S-matrix satisfy scalar field Schrödinger equation Schrödinger representation ſº solution space-time spin spinor string theory supersymmetry symmetry tangent space tensor term time-ordered torus vacuum vanish vector field vertex wave functional Weyl world-sheet zero modes

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Page vii - Frontiers in Physics" has been conceived in an effort to improve the situation in several ways. First, to take advantage of the fact that the leading physicists today frequently give a series of lectures, a graduate seminar, or a graduate course in their special fields of interest. Such lectures serve to summarize the present status of a rapidly developing field and may well constitute the only coherent account available at the time.

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Page iii - Frontiers in Physics David Pines, Editor Volumes of the Series published from 1961 to 1973 are not officially numbered. The parenthetical numbers shown are designed to aid librarians and bibliographers to check the completeness of their holdings. Titles published in this series prior to 1987 appear under either the WA Benjamin or the Benjamin/Cummings imprint; titles published since 1986 appear under the Westview Press imprint.

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