Heat Kernel and Quantum Gravity

Ivan G. Avramidi3540671552, 9783540671558

This book tackles quantum gravity via the so-called background field method and its effective action functional. The author presents an explicitly covariant and effective technique to calculate the de Witt coefficients and to analyze the Schwinger-de Wit asymptotic expansion of the effective action. He also investigates the ultraviolet behaviour of higher-derivative quantum gravity. The book addresses theoretical physicists, graduate students as well as researchers, but should also be of interest to physicists working in mathematical or elementary particle physics.

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Table of contents :
Cover……Page 1
Preface……Page 2
Contents……Page 4
Introduction……Page 6
1.1 Generating Functional, Green Functions and Effective Action……Page 13
1.2 Green Functions of Minimal Differential Operators……Page 18
1.3 Divergences, Regularization and Renormalization……Page 21
2.1 Covariant Expansions in Curved Space……Page 25
2.2 Elements of Covariant Expansions……Page 31
2.3 Technique for Calculation of De Witt Coefficients……Page 38
2.4 De Witt Coefficients a_3 and a_4……Page 41
2.5 Effective Action of Massive Fields……Page 50
3.1 Summation of Asymptotic Expansions……Page 54
3.2 Covariant Methods for Investigation of Nonlocalities……Page 56
3.3 Summation of First-Order Terms……Page 60
3.4 Summation of Second-Order Terms……Page 64
3.5 De Witt Coefficients in De Sitter Space……Page 71
4.1 Quantization of Gauge Field Theories……Page 80
4.2 One-Loop Divergences in Minimal Gauge……Page 86
4.3 One-Loop Divergences in Arbitrary Gauge and Vilkovisky’s Effective Action……Page 97
4.4 Renormalization Group and Ultraviolet Asymptotics……Page 104
4.5 Effective Potential……Page 111
Conclusion……Page 127
References……Page 129
Notation……Page 143
Index……Page 145
Back cover……Page 156