On Black Hole Creation in Planckian Energy Scattering

In a series of papers Amati, Ciafaloni and Veneziano and 't Hooft conjectured that black holes occur in the collision of two light particles at planckian energies. In this talk based on \cite {AVV} we discuss a possible scenario for such a process by using the Chandrasekhar-Ferrari-Xanthopoulos duality between the Kerr black hole solution and colliding plane gravitational waves.Comment: Cont.Proc. of VI Quantum Gravity Seminar, 15 pages, LATE

Why is Spacetime Lorentzian?

We expand on the idea that spacetime signature should be treated as a dynamical degree of freedom in quantum field theory. It has been argued that the probability distribution for signature, induced by massless free fields, is peaked at the Lorentzian value uniquely in D=4 dimensions. This argument is reviewed, and certain consistency constraints on the generalized signature (i.e. the tangent space metric \eta_{ab}(x)=\mbox{diag}[e^{i\theta(x)},1,1,1]) are derived. It is shown that only one dynamical "Wick angle" $\theta(x)$ can be introduced in the generalized signature, and the magnitude of fluctuations away from Lorentzian signature $\delta \theta = \pi - \theta$ is estimated to be of order $(l_P/R)^3$, where $l_P$ is the Planck length, and $R$ is the length scale of the Universe. For massless fields, the case of D=2 dimensions and the case of supersymmetry are degenerate, in the sense that no signature is preferred. Mass effects lift this degeneracy, and we show that a dynamical origin of Lorentzian signature is also possible for (broken) supersymmetry theories in D=6 dimensions, in addition to the more general non-supersymmetric case in D=4 dimensions.Comment: 26 pages, plain LaTeX, NBI-HE-93-3

Trying to understand confinement in the Schroedinger picture

We study the gauge-invariant gaussian ansatz for the vacuum wave functional and show that it potentially possesses many desirable features of the Yang--Mills theory, like asymptotic freedom, mass generation through the transmutation of dimensions and a linear potential between static quarks. We point out that these (and other) features can be studied in a systematic way by combining perturbative and 1/n expansions. Contrary to the euclidean approach, confinement can be easily formulated and easily built in, if not derived, in the variational Schroedinger approach.Comment: 21 pages, 1 figure. Lecture given at the 4th St.Petersburg Winter School in Theoretical Physics, Feb. 22-28, 199

Rolling in the Higgs Model and Elliptic Functions

Asymptotic methods in nonlinear dynamics are used to improve perturbation theory results in the oscillations regime. However, for some problems of nonlinear dynamics, particularly in the case of Higgs (Duffing) equation and the Friedmann cosmological equations, not only small oscillations regime is of interest but also the regime of rolling (climbing), more precisely the rolling from a top (climbing to a top). In the Friedman cosmology, where the slow rolling regime is often used, the rolling from a top (not necessary slow) is of interest too. In the present work a method for approximate solution to the Higgs equation in the rolling regime is presented. It is shown that in order to improve perturbation theory in the rolling regime turns out to be effective not to use an expansion in trigonometric functions as it is done in case of small oscillations but use expansions in hyperbolic functions instead. This regime is investigated using the representation of the solution in terms of elliptic functions. An accuracy of the corresponding approximation is estimated.Comment: Latex, 36 Pages, 8 figures, typos correcte

Dimension two vacuum condensates in gauge-invariant theories

Gauge dependence of the dimension two condensate in Abelian and non-Abelian Yang-Mills theory is investigated.Comment: 10 page

On Gauge Equivalence of Tachyon Solutions in Cubic Neveu-Schwarz String Field Theory

Simple analytic solution to cubic Neveu-Schwarz String Field Theory including the $GSO(-)$ sector is presented. This solution is an analog of the Erler-Schnabl solution for bosonic case and one of the authors solution for the pure $GSO(+)$ case. Gauge transformations of the new solution to others known solutions for the $NS$ string tachyon condensation are constructed explicitly. This gauge equivalence manifestly supports the early observed fact that these solutions have the same value of the action density.Comment: 8 pages, LaTe