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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
- 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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