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Hamada, Kenji. Quantum gravity and cosmology based on conformal field theory / by Ken-ji Hamada. — 1 online resource (xii, 397 pages) — <URL:http://elib.fa.ru/ebsco/2012289.pdf>.

Record create date: 1/29/2019

Subject: Quantum theory.; Cosmology.; Quantum gravity — Mathematics.; Field theory (Physics); Quantum theory.; Cosmology.; Field theory (Physics); Quantum gravity — Mathematics.; SCIENCE / Mechanics / General; SCIENCE / Mechanics / Solids

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Table of Contents

  • Table of Contents
  • Preface
  • Chapter One
    • Academic Interests
    • Historical Background
    • Excellent Points of The Theory
    • Outline of The Book
  • Chapter Two
    • Conformal Transformations
    • Conformal Algebra and Field Transformation Law
    • Correlation Functions and Positivity
    • Specific Examples of Positivity Conditions
    • Descendant Fields and Positivity
    • Feynman Propagators and Unitarity
  • Chapter Three
    • Critical Phenomena and Conformal Field Theory
    • Basic Structures
    • Rederivation of Two-Point Functions
    • Operator Product Expansions
    • Conformal Blocks
    • Casimir Operator and Conformal Blocks
    • Unitarity Bound Again
    • Unitarity Bounds from Conformal Bootstrap
    • Wilson-Fisher Epsilon-Expansion
  • Chapter Four
    • Virasoro Algebra and Unitary Representations
    • Virasoro Character and Partition Function on Torus
    • Free Boson Representation
  • Chapter Five
    • Wess-Zumino Integrability Condition
    • Liouville and Riegert Actions
    • Diffeomorphism Invariant Effective Actions
    • Toward BRST Conformal Symmetry
  • Chapter Six
    • Quantization of Liouville Action
    • Virasoro Algebra and Physical States
    • BRST Operator and Physical States
    • On Correlation Functions
  • Chapter Seven
    • Quantum Gravity Action
    • Diffeomorphism Invariance and Conformal Invariance
    • Quantization of Gravitational Field
      • Conformal-factor field
      • Traceless tensor field
    • Generators of Diffeomorphism
    • Conformal Algebra and Primary Fields
    • Physical Field Operators
    • BRST Formulation and Physical Conditions
      • Difference from conventional thinking
  • Chapter Eight
    • Canonical Quantization on R × S3
    • Generators of Conformal Transformations
    • BRST Operator and Physical State Conditions
    • Construction of Physical States
    • Physical Field Operators
    • State-Operator Correspondences and Dual States
  • Chapter Nine
    • Summary of Gravitational Counterterms
    • QED in Curved Space
    • Normal Products
    • Restrictions from Correlation Functions
    • Determination of Gravitational Counterterms
    • Determination of Conformal Anomalies
    • Casimir Energy
  • Chapter Ten
    • D-Dimensional Action and Renormalization Procedure
    • Kinetic Terms and Interactions
    • Gauge-Fixing
    • Calculations of Renormalization Factors
    • Background-Metric Independence Revisited
    • Diffeomorphism Invariant Effective Actions
    • Renormalization of Mass Parameters
    • Physical Cosmological Constant
  • Chapter Eleven
    • Instability and Evolution of Fluctuations
    • Friedmann Universe
  • Chapter Twelve
    • Inflation and Spacetime Phase Transition
    • Low Energy Effective Gravity Theory
  • Chapter Thirteen
    • Perturbation Variables
    • Evolution Equations of Fluctuations
      • Einstein Equations
      • Conservation Equations for Matter Fields
    • Fourier Transform of Evolution Equations
    • Solutions of Vector and Tensor Equations
      • Solutions in Physical Time
      • Solutions in Conformal Time
    • Solutions of Scalar EquationsWithout Baryons
      • Radiation-Dominated Era
      • Matter-Dominated Era
    • Solutions of Scalar Equations With Baryons
    • Evolution of Matter Fluctuations After Neutralization
  • Chapter Fourteen
    • Brief Summary After Big Bang
    • Evolution Equations in Quantum Gravity
    • Evolution Equations for Matter Fields
    • Initial Spectra of Quantum Gravity
    • Solutions of Evolution Equations and Stability
    • CMB Angular Power Spectra
  • Appendix A
    • Formulas on Curvatures
    • Scalar Fields in Curved Space
    • Fermions in Curved Space
    • Expansions of Gravitational Actions Around D = 4
  • Appendix B
    • Fourier Transform of Two-Point Function
    • Derivation of Critical Exponents
    • Conformal Algebra for Free Scalar on M4
    • Mapping to R × S3 Space
    • Two-Point Correlation Functions on R × S3
    • Correction Terms in Gauge-Fixed Conformal Transformations
    • Building Blocks for Vector and Tensor Fields
  • Appendix C
    • Spherical Tensor Harmonics on S3
    • SU(2) × SU(2) Clebsch-Gordan Coefficients
    • Product Formulas for Spherical Harmonics on S3
    • Formulas containing Clebsch-Gordan Coefficients and Wigner D-Functions
  • Appendix D
    • Useful Formulas in Dimensional Regularization
    • Examples of Renormalization Calculations in QED
    • Renormalization of Composite Scalar Fields
    • DeWitt-Schwinger Method
    • Dynamical Triangulation Method and Quantum Gravity
  • Appendix E
    • Sachs-Wolfe Effect
    • CMB Angular Power Spectra
    • Analytical Examinations of Evolution Equations
    • Scattering Cross Sections in Einstein Gravity
    • Fundamental Constants
  • Bibliography
  • Index

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