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

Includes bibliographical references and index.

Print version record.

Intro; 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 AgainUnitarity 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 InvarianceQuantization 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

Chapter TwelveInflation 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

Of Gravitational CountertermsQED 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

What is the world beyond the Planck scale that provides the minimum unit of the universe? The goal of quantum gravity is to reveal physical laws in such a world. There, quantum fluctuations of gravity become large, and what is called a background-free world where the concept of time and distance is lost shall be realized. The renormalizable quantum gravity introduced in this book offers a theory in which such a world is described by a certain conformal field theory and a deviation from there is handled as a perturbation. This is the state-of-the-art of modern physics that will help in understa.

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