Quantum Gravity, Quantum Cosmology and Lorentzian GeometriesSpringer Science & Business Media, 28. jan. 1994 - 349 síður This book is aimed at theoretical and mathematical physicists and mathematicians interested in modern gravitational physics. I have thus tried to use language familiar to readers working on classical and quantum gravity, paying attention both to difficult calculations and to existence theorems, and discussing in detail the current literature. The first aim of the book is to describe recent work on the problem of boundary conditions in one-loop quantum cosmology. The motivation of this research was to under stand whether supersymmetric theories are one-loop finite in the presence of boundaries, with application to the boundary-value problemsoccurring in quantum cosmology. Indeed, higher-loop calculations in the absence of boundaries are already available in the litera ture, showing that supergravity is not finite. I believe, however, that one-loop calculations in the presence of boundaries are more fundamental, in that they provide a more direct check of the inconsistency of supersymmetric quantum cosmology from the perturbative point of view. It therefore appears that higher-order calculations are not strictly needed, if the one-loop test already yields negative results. Even though the question is not yet settled, this research has led to many interesting, new applications of areas of theoretical and mathematical physics such as twistor theory in flat space, self-adjointness theory, the generalized Riemann zeta-function, and the theory of boundary counterterms in super gravity. I have also compared in detail my work with results by other authors, explaining, whenever possible, the origin of different results, the limits of my work and the unsolved problems. |
Efni
QUANTUM GRAVITY QUANTUM COSMOLOGY | 3 |
CANONICAL QUANTUM GRAVITY | 27 |
PERTURBATIVE QUANTUM GRAVITY | 53 |
GLOBAL BOUNDARY CONDITIONS AND 0 VALUE | 79 |
CHOICE OF BOUNDARY CONDITIONS IN ONELOOP | 103 |
GHOST FIELDS AND GAUGE MODES IN ONELOOP | 152 |
ADDENDUM TO CHAPTER SIX | 174 |
LOCAL BOUNDARY CONDITIONS FOR THE WEYL SPINOR | 188 |
LOCAL SUPERSYMMETRY IN PERTURBATIVE | 230 |
LORENTZIAN GEOMETRY Ự THEORIES | 245 |
CONCLUSIONS | 303 |
PROBLEMS FOR THE READER | 310 |
The Generalized ZetaFunction | 321 |
Lorentzian ADM Formulae for the Curvature | 328 |
REFERENCES | 335 |
ONELOOP RESULTS FOR THE SPIN1 FIELD | 214 |
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Ashtekar asymptotic expansion boundary-value problem canonical causality chapter classical coefficients conditions on S³ conjugate contribution curvature curves D'Eath defined definition degrees of freedom denote derivatives Dirac operator ECSK theory eigenvalue condition eigenvalues equation Esposito Euler-Maclaurin formula fermionic fields finite first-class constraints flat Euclidean formula function gauge modes gauge theories geodesics geometry Geroch ghost fields given global hyperbolicity Halliwell Hamiltonian Hawking and Ellis Hawking S. W. heat kernel Hehl implies linearized Lorentzian Louko manifold metric Moreover Moss obey obtained one-loop calculations path integral Penrose perturbative Phys physical Poincaré group Poletti prove quantization quantum cosmology quantum gravity relations result Riemannian scalar field Schleich second-class constraints singularity solution space space-time spacelike spin spinor supergravity supersymmetry technique theorem three-sphere timelike topology torsion transformations twistor values vanish vector whereas zeta-function