Keywords:
Quantum chromodynamics.
;
Electronic books.
Description / Table of Contents:
This book offers an introduction to Chiral Perturbation Theory. Coverage starts with the Lagrangian of the strong interactions and general symmetry principles, then develops the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors.
Type of Medium:
Online Resource
Pages:
1 online resource (345 pages)
Edition:
1st ed.
ISBN:
9783642192548
Series Statement:
Lecture Notes in Physics Series ; v.830
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=3067320
DDC:
530.14
Language:
English
Note:
Intro -- A Primer for Chiral Perturbation Theory -- Preface -- Contents -- 1 Quantum Chromodynamics and Chiral Symmetry -- 1.1…Some Remarks on SU(3) -- 1.2…Local Symmetries and the QCD Lagrangian -- 1.2.1 The QED Lagrangian -- 1.2.2 The QCD Lagrangian -- 1.3…Accidental, Global Symmetries of the QCD Lagrangian -- 1.3.1 Light and Heavy Quarks -- 1.3.2 Left-Handed and Right-Handed Quark Fields -- 1.3.3 Noether Theorem -- 1.3.4 Global Symmetry Currents of the Light-Quark Sector -- 1.3.5 The Chiral Algebra -- 1.3.6 Chiral Symmetry Breaking by the Quark Masses -- 1.4…Green Functions and Ward Identities -- 1.4.1 Ward Identities Resulting from U(1) Invariance: An Example -- 1.4.2 Chiral Green Functions -- 1.4.3 The Algebra of Currents -- 1.4.4 QCD in the Presence of External Fields and the Generating Functional -- 1.4.5 PCAC in the Presence of an External Electromagnetic Field -- References -- 2 Spontaneous Symmetry Breaking and the Goldstone Theorem -- 2.1…Degenerate Ground States -- 2.2…Spontaneous Breakdown of a Global, Continuous, Non-Abelian Symmetry -- 2.3…Goldstone Theorem -- 2.4…Explicit Symmetry Breaking: A First Look -- References -- 3 Chiral Perturbation Theory for Mesons -- 3.1…Effective Field Theory -- 3.2…Spontaneous Symmetry Breaking in QCD -- 3.2.1 The Hadron Spectrum -- 3.2.2 The Scalar Singlet Quark Condensate -- 3.3…Transformation Properties of the Goldstone Bosons -- 3.3.1 General Considerations -- 3.3.2 Application to QCD -- 3.4…Effective Lagrangian and Power-Counting Scheme -- 3.4.1 The Lowest-Order Effective Lagrangian -- 3.4.2 Symmetry Breaking by the Quark Masses -- 3.4.3 Construction of the Effective Lagrangian -- 3.4.4 Application at Lowest Order: Pion Decay -- 3.4.5 Application at Lowest Order: Pion-Pion Scattering -- 3.4.6 Application at Lowest Order: Compton Scattering -- 3.4.7 Dimensional Regularization.
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3.4.8 The Generation of Counter Terms -- 3.4.9 Power-Counting Scheme -- 3.5…Beyond Leading Order -- 3.5.1 The {{\fancyscript{O}}}(q^4) Lagrangian of Gasser and Leutwyler -- 3.5.2 Masses of the Goldstone Bosons at {{\fancyscript{O}}}(q^4) -- 3.5.3 The Effective Wess-Zumino-Witten Action -- 3.5.4 Chiral Perturbation Theory at {{\fancyscript{O}}}(q^6) -- References -- 4 Chiral Perturbation Theory for Baryons -- 4.1…Transformation Properties of the Fields -- 4.2…Baryonic Effective Lagrangian at Lowest Order -- 4.3…Applications at Lowest Order -- 4.3.1 Goldberger-Treiman Relation and the Axial-Vector Current Matrix Element -- 4.3.2 Pion-Nucleon Scattering -- 4.4…The Next-to-Leading-Order Lagrangian -- 4.5…Loop Diagrams: Renormalization and Power Counting -- 4.5.1 Counter Terms of the Baryonic ChPT Lagrangian -- 4.5.2 Power Counting -- 4.5.3 One-Loop Correction to the Nucleon Mass -- 4.6…Renormalization Schemes -- 4.6.1 Heavy-Baryon Approach -- 4.6.2 Infrared Regularization -- 4.6.3 Extended On-Mass-Shell Scheme -- 4.6.4 Dimensional Counting Analysis -- 4.7…The Delta Resonance -- 4.7.1 The Free Lagrangian of a Spin-3/2 System -- 4.7.2 Isospin -- 4.7.3 Leading-Order Lagrangian of the \Updelta(1232) Resonance -- 4.7.4 Consistent Interactions -- References -- 5 Applications and Outlook -- 5.1…Nucleon Mass and Sigma Term -- 5.1.1 Nucleon Mass to {\fancyscript{O}}(q^3) in the Heavy-Baryon Formalism -- 5.1.2 Nucleon Mass and Sigma Term at {\fancyscript{O}}(q^4) -- 5.1.3 Nucleon Mass Including the Delta Resonance -- 5.1.4 Nucleon Mass to {\fancyscript{O}}(q^6) -- 5.2…Nucleon Electromagnetic Form Factors to {\fancyscript{O}}(q^4) -- 5.3…Advanced Applications and Outlook -- 5.3.1 Chiral Extrapolationschiral extrapolation -- 5.3.2 Pion Photo- and Electroproductionpion production -- 5.3.3 Compton Scattering and PolarizabilitiesCompton scattering!nucleon.
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5.3.4 Virtual Compton ScatteringCompton scattering!virtual -- 5.3.5 Isospin-Symmetry Breakingisospin-symmetry breaking -- 5.3.6 Three-Flavor Calculations -- 5.3.7 Chiral Unitary Approacheschiral unitary approach -- 5.3.8 Complex-Mass Scheme -- 5.3.9 Chiral Effective Theory for Two- and Few-Nucleon Systemsfew-nucleon systems -- References -- Appendix A -- Appendix B -- Solutions to Exercises -- Index.
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