ISBN: 3-540-67155-2
TITLE: Heat Kernel and Quantum Gravity
AUTHOR: Avramidi, Ivan G.
TOC:

Introduction 1
1. Background Field Method in Quantum Field Theory 9
1.1 Generating Functional, Green Functions and Effective Action 9
1.2 Green Functions of Minimal Differential Operators 14
1.3 Divergences, Regularization and Renormalization 17
2. Technique for Calculation of De Witt Coefficients 21
2.1 Covariant Expansions in Curved Space 21
2.2 Elements of Covariant Expansions 27
2.3 Technique for Calculation of De Witt Coefficients 34
2.4 De Witt Coefficients a3 and a4 3 7
2.5 Effective Action of Massive Fields 46
3. Partial Summation of SchwingerDe Witt Expansion 51
3 .1 Summation of Asymptotic Expansions 51
3 .2 Covariant Methods for Investigation of Nonlocalities 53
3 .3 Summation of First-Order Terms 57
3 .4 Summation of Second-Order Terms 61
3 .5 De Witt Coefficients in De Sitter Space 68
4. Higher-Derivative Quantum Gravity 77
4.1 Quantization of Gauge Field Theories 77
4.2 One-Loop Divergences in Minimal Gauge 83
4.3 One-Loop Divergences in Arbitrary Gauge and Vilkovisky's Effective Action 94
4.4 Renormalization Group and Ultraviolet Asymptotics 101
4.5 Effective Potential 108
Conclusion 125
References 127
Notation 141
Index 143
END
