Heat Kernel and Quantum Gravity, Bindi 64Springer Science & Business Media, 27. mar. 2000 - 149 síður This book is aimed at theoretical as well as primarily physicists graduate students in field working quantum theory, quantum gravity, theories, gauge to sdme and and, it is not extent, general relativity cosmology. Although aimed at a I that it also be of level, hope in mathematically rigorous may terest to mathematical and mathematicians in physicists working spectral of differential mani geometry, spectral asymptotics on operators, analysis differential and mathematical methods in folds, geometry quantum theory. Thisbook will be considered too abstract some but certainly by physicists, not detailed and most mathematicians. This in completeenoughby means, thatthe material is at the level of particular, presented "physical" So, rigor. there theorems and areno and technicalcalculationsare lemmas, proofs long omitted. I tried detailed to a ofthe basic Instead, give presentation ideas, methodsandresults. Itried makethe to as andcom Also, exposition explicit as the lessabstractandhaveillustratedthe plete possible, methods language and results withsome As is well "onecannot examples. known, cover every in an text. The in this thing", especially introductory approach presented book the lines is a further of the so called along goes (and development) fieldmethod ofDe Witt. As a Ihavenot dealt at background consequence, allwithmanifoldswith boundary, non Laplacetype (ornonminimal) opera Riemann Cartan manifolds well with as as recent tors, developments many and advanced such Ashtekar's more as topics, approach, supergravity, strings, matrix etc. The membranes, interested reader is referred models, M theory tothe literature. |
Efni
Introduction | 1 |
1 Background Field Method in Quantum Field Theory | 9 |
2 Technique for Calculation of De Witt Coefficients | 21 |
3 Partial Summation of SchwingerDe Witt Expansion | 50 |
4 HigherDerivative Quantum Gravity | 77 |
Conclusion | 125 |
References | 127 |
Notation | 140 |
143 | |
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A.O. Barvinsky analytical continuation asymptotic expansion asymptotic freedom asymptotic series asymptotically free B.S. De Witt background field method Borel calculate coincidence limits coinciding points configuration space conformal anomalies conformal coupling conformal sector convergence coupling constant covariant derivatives curvature defined depend differential operators dimension dimensional E.S. Fradkin Einstein Euclidean action expression finite formfactors formulas G.A. Vilkovisky gauge theories gravitational field Green function heat kernel higher-derivative quantum gravity I.G. Avramidi integral Lett M.J. Duff mass shell matrix elements matter fields metric Moscow non-local Nucl obtain one-loop divergences one-loop effective action operator F order in background parameter perturbation theory Phys physical proper time method quadratic quantities quantized quantum field theory renormalization S-matrix scalar field Sect Sitter background Sitter space space-time standard effective action supergravity technique tensor theory of gravitation ultraviolet behavior ultraviolet divergences variables vector Vilkovisky's effective action Witt coefficients zero