Relativistic quantum field theory
Volume 2
Path integral formalism
Path integral formalism
Strickland, M. T. (Michael Thomas)
1969-
creator
author.
Morgan & Claypool Publishers
publisher.
Institute of Physics (Great Britain)
publisher.
text
bibliography
cau
2019
monographic
eng
access
1 online resource (various pagings) : illustrations (some color).
Volume 2 of this three-part series presents the quantization of classical field theory using the path integral formalism. For this volume the target audience is students who wish to learn about relativistic quantum field theory applied to particle physics, however, it is still very accessible and useful for students of condensed matter. This volume begins with the introduction of the path integral formalism for non-relativistic quantum mechanics and then, using this as a basis, extends the formalism to quantum fields with an infinite number of degrees of freedom. Dr. Strickland then discusses how to quantize gauge fields using the Fadeev-Popov method and fermionic fields using Grassman algebra. He then presents the path integral formulation of quantum chromodynamics and its renormalization. Finally, he discusses the role played by topological solutions in non-abelian gauge theories. Part of IOP Series in Nuclear Medicine.
1. Path integral formulation of quantum mechanics -- 1.1. The transition probability amplitude -- 1.2. Derivation of the quantum mechanical path integral -- 1.3. Path integral in terms of the Lagrangian -- 1.4. Computing simple path integrals -- 1.5. Calculating time-ordered expectation values -- 1.6. Adding sources -- 1.7. Asymptotic states and vacuum-vacuum transitions -- 1.8. Generating functional and Green's function for quadratic theories -- 1.9. Euclidean path integral and the statistical mechanics partition function
2. Path integrals for scalar fields -- 2.1. Generating functional for a free real scalar field -- 2.2. Interacting real scalar field theory -- 2.3. Generating functional for connected diagrams -- 2.4. The self-energy -- 2.5. The effective action and vertex functions -- 2.6. Generating function for one-particle irreducible graphs -- 2.7. Interacting complex scalar fields
3. Path integrals for fermionic fields -- 3.1. Finite-dimensional Grassmann algebra -- 3.2. Path integral for a free Dirac field -- 3.3. Path integral for an interacting Dirac field -- 3.4. Fermion loops
4. Path integrals for abelian gauge fields -- 4.1. Free abelian gauge theory -- 4.2. The photon propagator -- 4.3. Generating functional for abelian gauge fields in general Lorenz gauge -- 4.4. Generating functional for QED in general Lorenz gauge -- 4.5. General Lorenz-gauge QED generating functional to O(e2) -- 4.6. QED effective action and vertex functions -- 4.7. Ward-Takahashi identities
5. Groups and Lie groups -- 5.1. Group theory basics -- 5.2. Examples -- 5.3. Representations of groups -- 5.4. The group U(1) -- 5.5. The group SU(2) -- 5.6. The group SU(3) -- 5.7. The group SU(N) -- 5.8. The Haar measure
6. Path integral formulation of quantum chromodynamics -- 6.1. The Fadeev-Popov method -- 6.2. QCD Feynman rules -- 6.3. Simple example application of the QCD Feynman rules -- 6.4. Becchi, Rouet, Stora, and Tyutin symmetry -- 6.5. Slavnov-Taylor identities
7. Renormalization of QCD -- 7.1. Divergences in scalar field theories -- 7.2. Divergences in Yang-Mills theory -- 7.3. Dimensional regularization refresher -- 7.4. One-loop renormalization of QCD -- 7.5. The one-loop QCD running coupling
8. Topological objects in field theory -- 8.1. The kinky sine-Gordon model -- 8.2. Two-dimensional vortex lines -- 8.3. Topological solutions in Yang-Mills -- 8.4. The instanton -- 8.5. The Potryagin index -- 8.6. Explicit solution for a q = 1 instanton -- 8.7. Quantum tunneling, [theta]-vacua, and symmetry breaking -- 8.8. Quantum anomalies -- 8.9. An effective Lagrangian for the anomaly -- 8.10. Instantons and the chiral anomaly -- 8.11. Perturbation theory for the chiral anomaly.
Michael Strickland.
"Version: 20191101"--Title page verso.
"A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.
Also available in print.
System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
Includes bibliographical references.
Dr. Strickland is a professor of physics at Kent State University. His primary interest is the physics of the quark-gluon plasma (QGP) and high-temperature quantum field theory (QFT). The QGP is predicted by quantum chromodynamics (QCD) to have existed until approximately 10-5seconds after the big bang. Dr. Strickland has published research papers on various topics related to the QGP, quantum field theory, relativistic hydrodynamics, and many other topics. In addition, he has co-written a classic text on the physics of neural networks.
Relativistic quantum theory
Quantum field theory
Quantum physics (quantum mechanics & quantum field theory)
SCIENCE / Physics / Quantum Theory
QC174.24.R4 .S777 2019eb vol. 2
530.12
IOP (Series)
Release 6
IOP concise physics
IOP series in nuclear spectroscopy and nuclear structure
9781643277080
9781643277066
9781643277059
https://iopscience.iop.org/book/978-1-64327-708-0
CaBNVSL
191209
20191210212358.0
12385510
eng