Quantum Electro and Chromodynamics treated by Thompson's heuristic approach

In this work we apply Thompson's method (of the dimensions and scales) to study some features of the Quantum Electro and Chromodynamics. This heuristic method can be considered as a simple and alternative way to the Renormalisation Group (R.G.) approach and when applied to QED-lagrangian is able to obtain in a first approximation both the running coupling constant behavior of alpha(mu) and the mass m(mu).The calculations are evaluated just at d_c=4, where d_c is the upper critical dimension of the problem, so that we obtain the logarithmic behavior both for the coupling alpha and the excess of mass Delta m on the energy scale mu. Although our results are well-known in the vast literature of field theories,it seems that one of the advantages of Thompson's method, beyond its simplicity is that it is able to extract directly from QED-lagrangian the physical (finite) behavior of alpha(mu) and m(mu), bypassing hard problems of divergences which normally appear in the conventional renormalisation schemes applied to field theories like QED. Quantum Chromodynamics (QCD) is also treated by the present method in order to obtain the quark condensate value. Besides this, the method is also able to evaluate the vacuum pressure at the boundary of the nucleon. This is done by assumming a step function behavior for the running coupling constant of the QCD, which fits nicely to some quantities related to the strong interaction evaluated through the MIT-bag model.Comment: RevTex, 25 pages, no figure

On Field Theoretic Generalizations of a Poisson Algebra

A few generalizations of a Poisson algebra to field theory canonically formulated in terms of the polymomentum variables are discussed. A graded Poisson bracket on differential forms and an $(n+1)$-ary bracket on functions are considered. The Poisson bracket on differential forms gives rise to various generalizations of a Gerstenhaber algebra: the noncommutative (in the sense of Loday) and the higher-order (in the sense of the higher order graded Leibniz rule). The $(n+1)$-ary bracket fulfills the properties of the Nambu bracket including the ``fundamental identity'', thus leading to the Nambu-Poisson algebra. We point out that in the field theory context the Nambu bracket with a properly defined covariant analogue of Hamilton's function determines a joint evolution of several dynamical variables.Comment: 10 pages, LaTeX2e. Missprint in Ref. 1 is corrected (hep-th/9709229 instead of ...029

Quantum-mechanical model of the Kerr-Newman black hole

We consider a Hamiltonian quantum theory of stationary spacetimes containing a Kerr-Newman black hole. The physical phase space of such spacetimes is just six-dimensional, and it is spanned by the mass $M$, the electric charge $Q$ and angular momentum $J$ of the hole, together with the corresponding canonical momenta. In this six-dimensional phase space we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Kerr-Newman black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator and an eigenvalue equation for the Arnowitt-Deser-Misner (ADM) mass of the hole, from the point of view of a distant observer at rest, is obtained. In a certain very restricted sense, this eigenvalue equation may be viewed as a sort of "Schr\"odinger equation of black holes". Our "Schr\"odinger equation" implies that the ADM mass, electric charge and angular momentum spectra of black holes are discrete, and the mass spectrum is bounded from below. Moreover, the spectrum of the quantity $M^2-Q^2-a^2$, where $a$ is the angular momentum per unit mass of the hole, is strictly positive when an appropriate self-adjoint extension is chosen. The WKB analysis yields the result that the large eigenvalues of $M$, $Q$ and $a$ are of the form $\sqrt{2n}$, where $n$ is an integer. It turns out that this result is closely related to Bekenstein's proposal on the discrete horizon area spectrum of black holes.Comment: 30 pages, 3 figures, RevTe

Building blocks of a black hole

What is the nature of the energy spectrum of a black hole ? The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As stressed long ago by by Mukhanov, such eigenvalues must be exponentially degenerate with respect to the area quantum number if one is to understand black hole entropy as reflecting degeneracy of the observable states. Here we construct the black hole states by means of a pair of "creation operators" subject to a particular simple algebra, a slight generalization of that for the harmonic oscillator. We then prove rigorously that the n-th area eigenvalue is exactly 2 raised to the n-fold degenerate. Thus black hole entropy qua logarithm of the number of states for fixed horizon area comes out proportional to that area.Comment: PhysRevTeX, 14 page

Kondo effect in a double quantum-dot molecule under the effect of an electric and magnetic field

Electron tunneling through a double quantum dot molecule, in the Kondo regime, under the effect of a magnetic field and an applied voltage, is studied. This system possesses a complex response to the applied fields characterized by a tristable solution for the conductance. The different nature of the solutions are studied in and out thermodynamical equilibrium. It is shown that the interdot coupling and the fields can be used to control the region of multistability. The mean-field slave-boson formalism is used to obtain the solution of the problem.Comment: 5 pages, 4 figures. To appear in Sol. State Com

Microcanonical statistics of black holes and bootstrap condition

The microcanonical statistics of the Schwarzschild black holes as well as the Reissner-Nordstr$\sf \ddot{o}$m black holes are analyzed. In both cases we set up the inequalities in the microcanonical density of states. These are then used to show that the most probable configuration in the gases of black holes is that one black hole acquires all of the mass and all of the charge at high energy limit. Thus the black holes obey the statistical bootstrap condition and, in contrast to the other investigation, we see that U(1) charge does not break the bootstrap property.Comment: 16 pages. late

BPS black holes, quantum attractor flows and automorphic forms

We propose a program for counting microstates of four-dimensional BPS black holes in N >= 2 supergravities with symmetric-space valued scalars by exploiting the symmetries of timelike reduction to three dimensions. Inspired by the equivalence between the four dimensional attractor flow and geodesic flow on the three-dimensional scalar manifold, we radially quantize stationary, spherically symmetric BPS geometries. Connections between the topological string amplitude, attractor wave function, the Ooguri-Strominger-Vafa conjecture and the theory of automorphic forms suggest that black hole degeneracies are counted by Fourier coefficients of modular forms for the three-dimensional U-duality group, associated to special "unipotent" representations which appear in the supersymmetric Hilbert space of the quantum attractor flow.Comment: 9 pages, revtex; v2: references added and typos correcte

Tristability in a non-equilibrium double-quantum-dot in Kondo regime

Electron tunneling through a non-equilibrium double quantum dot in the Kondo regime is studied. In the region of negative differential resistance, it is shown that this system possesses a complex response to the applied potential characterized by a tristable solution for the current. Increasing the applied potential or reducing the inter-dot coupling, the system goes through a transition from a coherent inter-dot regime to an incoherent one. The different nature of the solutions are characterized and it is shown that the effects of the asymmetry in the dot-lead coupling can be used to control the region of multistability. The mean-field slave-boson formalism is used to obtain the solution of the problem.Comment: 4 pages, 4 figures. To appear in Sol. State. Com

Semiclassical Black Hole States and Entropy

We discuss semiclassical states in quantum gravity corresponding to Schwarzschild as well as Reissner Nordstr\"om black holes. We show that reduced quantisation of these models is equivalent to Wheeler-DeWitt quantisation with a particular factor ordering. We then demonstrate how the entropy of black holes can be consistently calculated from these states. While this leads to the Bekenstein-Hawking entropy in the Schwarzschild and non-extreme Reissner-Nordstr\"om cases, the entropy for the extreme Reissner-Nordstr\"om case turns out to be zero.Comment: Revtex, 15 pages, some clarifying comments and additional references included, to appear in Phys. Rev.

Lifetime of metastable states in resonant tunneling structures

We investigate the transport of electrons through a double-barrier resonant-tunneling structure in the regime where the current-voltage characteristics exhibit bistability. In this regime one of the states is metastable, and the system eventually switches from it to the stable state. We show that the mean switching time grows exponentially as the voltage across the device is tuned from the its boundary value into the bistable region. In samples of small area we find that the logarithm of the lifetime is proportional to the voltage (measured from its boundary value) to the 3/2 power, while in larger samples the logarithm of the lifetime is linearly proportional to the voltage.Comment: REVTeX 4, 5 pages, 3 EPS-figure