Quantum gravity and cosmology based on conformal field theory / by Ken-ji Hamada.

Format:

Book

Author/Creator:

Hamada, Kenji, 1962- author.

Contributor:

Craig M. Merrihue Memorial Fund.

Language:

English

Japanese

Subjects (All):

Quantum theory.

Cosmology.

Quantum gravity--Mathematics.

Quantum gravity.

Field theory (Physics).

Physical Description:

xii, 397 pages ; 21 cm

Place of Publication:

Newcastle upon Tyne, UK : Cambridge Scholars Publishing, 2018.

Contents:

Academic Interests p. 2

Excellent Points of The Theory p. 5

Chapter 2 Conformal Field Theory in Minkowski Space p. 11

Conformal Transformations p. 11

Conformal Algebra and Field Transformation Law p. 13

Correlation Functions and Positivity p. 17

Specific Examples of Positivity Conditions p. 20

Descendant Fields and Positivity p. 22

Feynman Propagators and Unitarity p. 23

Chapter 3 Conformal Field Theory in Euclidean Space p. 27

Critical Phenomena and Conformal Field Theory p. 27

Basic Structures p. 28

Rederivation of Two-Point Correlation Function p. 32

Three- and Four-Point Scalar Correlation Functions p. 33

Operator Product Expansions p. 34

Conformal Blocks p. 37

Casimir Operator and Conformal Blocks p. 41

Unitarity Bound Again p. 42

Unitarity Bounds from Conformal Bootstrap p. 45

Wilson-Fisher Epsilon-Expansion p. 49

Chapter 4 Basis of Two-Dimensional Conformal Field Theory p. 51

Virasoro Algebra and Unitary Representations p. 51

Virasoro Character and Partition Function on Torus p. 56

Free Boson Representation p. 59

Chapter 5 Conformal Anomaly and Wess-Zumino Action p. 65

Wess-Zumino Integrability Condition p. 65

Liouville and Riegert Actions p. 67

Diffeomorphism Invariant Effective Actions p. 69

Toward BRST Conformal Symmetry p. 71

Chapter 6 Two-Dimensional Quantum Gravity p. 73

Quantization of Liouville Action p. 73

Virasoro Algebra and Physical States p. 76

BRST Operator and Physical States p. 81

On Correlation Functions p. 85

Chapter 7 Background-Free Quantum Gravity p. 87

Quantum Gravity Action p. 87

Diffeomorphism Invariance and Conformal Invariance p. 92

Quantization of Gravitational Field p. 94

Conformal-Factor Field p. 95

Traceless Tensor Field p. 99

Generators of Diffeomorphism p. 104

Conformal Algebra and Primary Fields p. 107

Physical Field Operators p. 112

BRST Formulation and Physical Conditions p. 114

Difference from conventional thinking p. 117

Chapter 8 Physical States of Quantum Gravity p. 119

Canonical Quantization on R × S³ p. 119

Generators of Conformal Transformations p. 126

BRST Operator and Physical State Conditions p. 135

Construction of Physical States p. 140

Physical Field Operators p. 146

State-Operator Correspondence and Dual States p. 149

Chapter 9 Gravitational Counterterms and Conformal Anomalies p. 153

Summary of Gravitational Counterterms p. 153

QED in Curved Space p. 156

Normal Products p. 160

Restrictions from Correlation Functions p. 166

Determination of Gravitational Counterterms p. 177

Determination of Conformal Anomalies p. 181

Casimir Energy p. 182

Chapter 10 Renormalization in Quantum Gravity p. 185

D-Dimensional Action and Renormalization Procedure p. 185

Kinetic Terms and Interactions p. 192

Gauge-Fixing p. 197

Calculations of Renormalization Factors p. 200

Background-Metric Independence Revisited p. 214

Diffeomorphism Invariant Effective Actions p. 216

Renormalization of Mass Parameters p. 219

Physical Cosmological Constant p. 225

Chapter 11 The Universe in Einstein Gravity p. 231

Instability and Evolution of Fluctuations p. 231

Friedmann Universe p. 234

Chapter 12 Quantum Gravity Cosmology p. 241

Inflation and Spacetime Phase Transition p. 241

Low Energy Effective Gravity Theory p. 247

Chapter 13 Cosmological Perturbation Theory p. 253

Perturbation Variables p. 253

Evolution Equations of Fluctuations p. 258

Einstein Equations p. 258

Conservation Equations for Matter Fields p. 263

Fourier Transform of Evolution Equations p. 264

Adiabatic Conditions p. 265

Solutions of Vector and Tensor Equations p. 267

Solutions in Physical Time p. 267

Solutions in Conformal Time p. 268

Solutions of Scalar Equations Without Baryons p. 270

Radiation-Dominated Era p. 270

Matter-Dominated Era p. 272

Solutions of Scalar Equations With Baryons p. 275

Evolution of Matter Fluctuations After Neutralization p. 281

Chapter 14 From Quantum Gravity to CMB p. 283

Brief Summary After Big Bang p. 283

Evolution Equations in Quantum Gravity p. 284

Evolution Equations for Matter Fields p. 288

Initial Spectra of Quantum Gravity p. 290

Solutions of Evolution Equations and Stability p. 292

CMB Angular Power Spectra p. 297.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Craig M. Merrihue Memorial Fund.

ISBN:

9781527513716

1527513718

OCLC:

1047550661

Publisher Number:

99977966897