Quantum Field Theory

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2007-02-05
  • Publisher: Cambridge University Press

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Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497.

Table of Contents

Preface for students
Preface for instructors
Spin Zero
Attempts at relativistic quantum mechanics
Lorentz invariance
Canonical quantization of scalar fields
The spin-statistics theorem
The LSZ reduction formula
Path integrals in quantum mechanics
The path integral for the harmonic oscillator
The path integral for free field theory
The path integral for interacting field theory
Scattering amplitudes and the Feynman rules
Cross sections and decay rates
Dimensional analysis with ?=c=1
The Lehmann-Kll(c)n form
Loop corrections to the propagator
The one-loop correction in Lehmann-Kll(c)n form
Loop corrections to the vertex
Other 1PI vertices
Higher-order corrections and renormalizability
Perturbation theory to all orders
Two-particle elastic scattering at one loop
The quantum action
Continuous symmetries and conserved currents
Discrete symmetries: P, T, C, and Z
Nonabelian symmetries
Unstable particles and resonances
Infrared divergences
Other renormalization schemes
The renormalization group
Effective field theory
Spontaneous symmetry breaking
Broken symmetry and loop corrections
Spontaneous breaking of continuous symmetries
Spin One Half
Representations of the Lorentz Group
Left- and right-handed spinor fields
Manipulating spinor indices
Lagrangians for spinor fields
Canonical quantization of spinor fields I
Spinor technology
Canonical quantization of spinor fields II
Parity, time reversal, and charge conjugation
LSZ reduction for spin-one-half particles
The free fermion propagator
The path integral for fermion fields
Formal development of fermionic path integrals
The Feynman rules for Dirac fields
Spin sums
Gamma matrix technology
Spin-averaged cross sections
The Feynman rules for majorana fields
Massless particles and spinor helicity
Loop corrections in Yukawa theory
Beta functions in Yukawa theory
Functional determinants
Spin One
Maxwell's equations
Electrodynamics in coulomb gauge
LSZ reduction for photons
The path integral for photons
Spinor electrodynamics
Scattering in spinor electrodynamics
Spinor helicity for spinor electrodynamics
Scalar electrodynamics
Loop corrections in spinor electrodynamics
The vertex function in spinor electrodynamics
The magnetic moment of the electron
Loop corrections in scalar electrodynamics
Beta functions in quantum electrodynamics
Ward identities in quantum electrodynamics I
Ward identities in quantum electrodynamics II
Nonabelian gauge theory
Group representations
The path integral for nonabelian gauge theory
The Feynman rules for nonabelian gauge theory
The beta function for nonabelian gauge theory
BRST symmetry
Chiral gauge theories and anomalies
Anomalies in global symmetries
Anomalies and the path integral for fermions
Background field gauge
Gervais-Neveu gauge
The Feynman rules for N x N matrix fields
Scattering in quantum chromodynamics
Wilson loops, lattice theory, and confinement
Chiral symmetry breaking
Spontaneous breaking of gauge symmetries
Spontaneously broken abelian gauge theory
Spontaneously broken nonabelian gauge theory
The standard model: Gauge and Higgs sector
The standard model: Lepton sector
The standard model: Quark sector
Electroweak interactions of hadrons
Neutrino masses
Solitons and monopoles
Instantons and theta vacua
Quarks and theta vacua
The minimal supersymmetric standard model
Grand unification
Table of Contents provided by Publisher. All Rights Reserved.

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