## Field TheoryPresents recent advances of perturbative relativistic field theory in a pedagogical and straightforward way. For graduate students who intend to specialize in high-energy physics. |

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### Contents

How to Build an Action Functional | 1 |

The Action Functional in Quantum Mechanics | 45 |

The Feynman Path Integral in Field Theory | 63 |

6 THEORY | 101 |

Path Integral Formulation with Fermions | 161 |

YangMills and Gravity | 183 |

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### Common terms and phrases

Abelian Action anomaly antisymmetric arbitrary asymptotic chiral classical coefficients compute conserved contribution convergent corresponding counterterms coupling constant covariant derivative defined depend dimensionless Dirac spinor eigenvalues equations of motion Euclidean space evaluate expression fermion Feynman diagrams Feynman rules field theory finite formula four dimensions gauge fields gauge invariance gauge theories gauge transformation given Grassmann Green's functions Hamiltonian Hence Hermitian indices infinitesimal infrared divergence integrand interaction kinetic term Lagrangian Lie algebra Lorentz transformations Majorana mass matrix Minkowski space momenta momentum Note obtain operator parameters particle path integral photon Phys physical Poincaré Poincaré group pole prescription problem propagator Quantum Mechanics quarks renormalizable renormalization representation result rewrite ſ dºr scalar field scale ſº solutions spin spinor fields SU(n supersymmetry symmetry tensor transition amplitude vanishes variables vector vertex zero

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Page xi - The enormous growth in the number of physicists has tended to make the familiar channels of communication considerably less effective. It has become increasingly difficult for experts in a given field to keep up with the current literature; the novice can only be confused. What is needed is both a consistent account of a field and the presentation of a definite "point of view

Page xi - ... point of view" concerning it. Formal monographs cannot meet such a need in a rapidly developing field, and, perhaps more important, the review article seems to have fallen into disfavor. Indeed, it would seem that the people most actively engaged in developing a given field are the people least likely to write at length about it. "Frontiers in Physics" has been conceived in an effort to improve the situation in several ways.

Page vii - 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.

Page xi - 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. Often, notes on lectures exist (prepared by the lecturer himself,...

Page ix - Theory of Nonneutral Plasmas, 1974 Green's Functions for Solid State Physicists, 1974 Dual Resonance Models, 1974 Modern Theory of Critical Phenomena, 1976 Hydrodynamic Fluctuation, Broken Symmetry, and Correlation Functions, 1975 Qualitative Methods in Quantum Theory, 1977 Condensed Matter Physics: Dynamic Correlations, 1980 Gauge Fields: Introduction to Quantum Theory, 1980 Field Theory: A Modern Primer, 1981 [cf. 74 — 2nd ed.] Heavy Ion Reactions: Lecture Notes Vol.

Page viii - Current, 1967 Current Algebras and Applications to Particle Physics, 1968 Nuclear Theory: The Quasiparticle Method, 1968 The Quark Model, 1969 Approximation Methods in Quantum Mechanics, 1969 Nonlinear Plasma Theory, 1969 Quantum Kinematics and Dynamics, 1970 Statistical Mechanics: A Set of Lectures, 1972...

Page vii - Nuclear Magnetic Relaxation: A Reprint Volume, 1961 S-Matrix Theory of Strong Interactions: A Lecture Note and Reprint Volume, 1961 Quantum Electrodynamics: A Lecture Note and Reprint Volume The Theory of Fundamental Processes: A Lecture Note Volume, 1961 Problem in Quantum Theory of Many-Particle Systems: A Lecture Note and Reprint Volume, 1961 The Many-Body Problem: A Lecture Note and Reprint Volume, 1961 The Mossbauer Effect: A Review — With a Collection of Reprints, 1962 Quantum Statistical...

Page xi - Physics was conceived in 1961 in an effort to improve the situation in several ways. Leading physicists 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. One of the principal purposes of the Frontiers in Physics...

Page viii - Review-With a Collection of Reprints), 1964 Strong-Interaction Physics: A Lecture Note Volume, 1964 Theory of Interacting Fermi Systems, 1964 Theory of Superconductivity, 1964 (revised 3rd printing, 1983) Nonlinear Optics: A Lecture Note and Reprint Volume, 1965 Phase Transitions, 1965 An Introduction to the Theory of Superfluidity, 1965 Superconductivity of Metals and Alloys, 1966 Pseudopotentials in the Theory of Metals, 1966 Phenomenological Theories of High Energy Scattering: An Experimental...

Page viii - Interactions, 1972 Combinatorics and Renormalization in Quantum Field Theory, 1973 The Redshift Controversy, 1973 Hadron Physics at Very High Energies, 1973 Basic Principles of Plasma Physics: A Statistical Approach, 1973 (2nd printing, with revisions, 1980) The Physical Principles of Electron Paramagnetic Resonance, 2nd Edition, completely revised, enlarged, and reset, 1973 [cf. (9>— 1st edition] Volumes published from 1974 onward are being numbered as an integral part of the bibliography.