Download Quantum gravity

QUANTUM GRAVITY
Educational-Scientific Institute of Gravitation and Cosmology, PFUR
Obligatory course for 5th and 6th course students. Lectures: 48 h.
Aim
Approaches to quantum gravity and its applications in black hole physics and
cosmology.
Theme 1. Classification of quantizations of gravity
Zelmanov's cube. Fundamental constants. Planck units. Compton length,
gravitational and Bohr radiuses. Quantum mechanics and quantum field theory in
curved space-time. Quantum geometrodynamics. Quantization of weak
gravitational fields. Loop quantum gravity. Supergravity. Superstrings theory.
Theme 2. Basic General Relativity
Riemannian space metric. Christoffel symbols. Curvature tensor. Covariant
derivative. Tensor of macroscopic bodies. Energy conservation law. Bianchi
identities. Einstein equations. Spherical and axial-symmetric solutions.
Gravitational fields generated by mass, charge and angular momentum.
Theme 3. Classical effects in sperically-symmetric gravitational fields
Schwarzschild and Reissner-Nordstrom metrics. Gravitational attraction linked to
mass and gravitational repulsing linked to charge. Trajectory and law of test
particle motion. Einstein-Doppler effect. White holes. Motion and radiation of
charged particle in Schwarzschild field. DeWitt's interaction force and its
interpretation. Link between charged particle motion in Schwarzschild field and
motion of neutral particle of the same mass in effective Reissner-Nordstrom field.
Bending of charged particle worldline from geodesic in Schwarzschild field.
Тheme 4. Quantum mechanics of charged particle in Schwarzschild field
Schrodinger equation in curved spacetime. Nonrelativistic case – DeWitt's force.
Graviatom. Waves functions & energy spectrum. Hydrogen-like & oscillator
limits.
Theme 5. Electromagnetic and gravitational radiation of graviatoms
Electric dipol, quadrupol, gravitational quadrupol radiation of Hydrogen atom and
graviatom. Characteristic sizes of system, characteristic frequences of radiation.
Oscillator forces. Intensities of radiation.
Theme 6. Quantum geometrodynamics
Peres equation. Superspace. Wheeler-DeWitt equation in 3-spaces space. Wheeler
-DeWitt equation in minisuperspace. Hamiltonian constraint.
Theme 7. Quantum cosmology
Quantization of Friedmann equations for multicomponent medium. Birth of
Universe by tunneling. Energy levels and probability of Universe birth. Parameters
of quantum cosmological models and their limitations by observational cosmology.
Universe birth in laboratory. Quantum-gravitational collapse. Quantization of
anisotropic cosmological models.
Theme 8. Quantum field theory in curved space-time
Casimir effect. Effective temperature of vacuum. Hawking effect. Black holes
steam. Unruh effect. Rindler horizon. Link between effective temperature of
vacuum and thermal Green function. Particles birth. Bogoliubov transformations.
Particles birth in Friedmann models. Eddington model. Quantum field theory for
bosons and fermions in curved space-time. Conformal transformations.
Bibliography
Basic
1. C. Misner, K. Thorne, J. Wheeler Gravitation (1977)
2. Ya.B. Zeldovich, I.D. Novikov Gravity theory and stellar evolution (1971)
3. L.D. Landau, E.M. Lifshitz Field theory
4. Ya.B. Zeldovich, I.D. Novikov Creation and evolution of Universe (1975)
5. A.D. Dolgov, Ya.B. Zeldovich, M.V. Sazhin Early Universe
Cosmology(1988)
6. L.D. Landau, E.M. Lifshitz Quantum mechanics. Nonrelativistic theory
(1963)
7. A.A. Grib, S.G. Mamaev, V.M. Mostepanenko Quantum effects in intensive
internal fields (1980)
Additional
1. S. Weinberg Gravitation and Cosmology (1975)
2. A.D. Linde Elementary particle physics and inflationary cosmology (1990)
3. I.D. Novikov How growed the Universe(1988)
4. J.A. Wheeler Einsteins Vision (1970)
5. V.M. Mostepanenko, N.N. Trunov Casimir Effect (1990)
Composer: M.L. Filchenkov, PhD, Ass. Professor of ESIGC PFUR