Effective Gravitational Field of Black Holes

The problem of interpretation of the \hbar^0-order part of radiative corrections to the effective gravitational field is considered. It is shown that variations of the Feynman parameter in gauge conditions fixing the general covariance are equivalent to spacetime diffeomorphisms. This result is proved for arbitrary gauge conditions at the one-loop order. It implies that the gravitational radiative corrections of the order \hbar^0 to the spacetime metric can be physically interpreted in a purely classical manner. As an example, the effective gravitational field of a black hole is calculated in the first post-Newtonian approximation, and the secular precession of a test particle orbit in this field is determined.Comment: 8 pages, LaTeX, 1 eps figure. Proof of the theorem and typos correcte

Character Expansion Methods for Matrix Models of Dually Weighted Graphs

We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large $N$ limit of the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphs possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problem of phase transitions from random to flat lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into the text in Pictex commands. (Two minor math typos corrected. Acknowledgements added.

Some New/Old Approaches to QCD

This is a talk delivered at the Meeting on Integrable Quantum Field Theories, Villa Olmo and at STRINGS 1992, Rome, September 1992. I discuss some recent attempts to revive two old ideas regarding an analytic approach to QCD-the development of a string representation of the theory and the large N limit of QCD.Comment: 20 page

Quantum Fluctuations of Coulomb Potential as a Source of Flicker Noise. The Influence of External Electric Field

Fluctuations of the electromagnetic field produced by quantized matter in external electric field are investigated. A general expression for the power spectrum of fluctuations is derived within the long-range expansion. It is found that in the whole measured frequency band, the power spectrum of fluctuations exhibits an inverse frequency dependence. A general argument is given showing that for all practically relevant values of the electric field, the power spectrum of induced fluctuations is proportional to the field strength squared. As an illustration, the power spectrum is calculated explicitly using the kinetic model with the relaxation-type collision term. Finally, it is shown that the magnitude of fluctuations produced by a sample generally has a Gaussian distribution around its mean value, and its dependence on the sample geometry is determined. In particular, it is demonstrated that for geometrically similar samples, the power spectrum is inversely proportional to the sample volume. Application of the obtained results to the problem of flicker noise is discussed.Comment: 14 pages, 3 figure

Verification of CPT-invariance of QED bound states for the production of muonium or antimuonium in scattering of electrons or positrons by nuclei

A possibility of a verification of CPT-invariance of QED for bound states by example of muonium or antimuonium produced in reactions of scattering of electrons or positrons by nuclei is considered. The number of events of the muonium production is estimated for contemporary accelerators. The method of the detection of muonium by measuring of oscillations of the decay curve caused by the interference between the ground and excited state of muonium is suggested. The admixture of the excited muonium to the final state is calculated.Comment: 7 pages, 3 figures, Latex, published in JETP 74, 196 (2001), corrected mistypes in eqs. (2.2), (2.4), (2.7