Effective Polymer Dynamics of D-Dimensional Black Hole Interiors

We consider two different effective polymerization schemes applied to D-dimensional, spherically symmetric black hole interiors. It is shown that polymerization of the generalized area variable alone leads to a complete, regular, single-horizon spacetime in which the classical singularity is replaced by a bounce. The bounce radius is independent of rescalings of the homogeneous internal coordinate, but does depend on the arbitrary fiducial cell size. The model is therefore necessarily incomplete. It nonetheless has many interesting features: After the bounce, the interior region asymptotes to an infinitely expanding Kantowski-Sachs spacetime. If the solution is analytically continued across the horizon, the black hole exterior exhibits asymptotically vanishing quantum-corrections due to the polymerization. In all spacetime dimensions except four, the fall-off is too slow to guarantee invariance under Poincare transformations in the exterior asymptotic region. Hence the four-dimensional solution stands out as the only example which satisfies the criteria for asymptotic flatness. In this case it is possible to calculate the quantum-corrected temperature and entropy. We also show that polymerization of both phase space variables, the area and the conformal mode of the metric, generically leads to a multiple horizon solution which is reminiscent of polymerized mini-superspace models of spherically symmetric black holes in Loop Quantum Gravity.Comment: 14 pages, 4 figures. Added discussion about the dependency on auxiliary structures. Matches with the published versio

Role of causality in ensuring unconditional security of relativistic quantum cryptography

The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not employ collective measurements and quantum codes, the cryptosystem can be experimentally realized with the present state-of-art in fiber optics technologies. The proposed cryptosystem employs only the individual measurements and classical codes and, in addition, the key distribution problem allows to postpone the choice of the state encoding scheme until after the states are already received instead of choosing it before sending the states into the communication channel (i.e. to employ a sort of ``antedate'' coding).Comment: 9 page

Light-Cone Quantization of the Liouville Model

We present the quantization of the Liouville model defined in light-cone coordinates in (1,1) signature space. We take advantage of the representation of the Liouville field by the free field of the Backl\"{u}nd transformation and adapt the approch by Braaten, Curtright and Thorn. Quantum operators of the Liouville field $\partial_{+}\phi$, $\partial_{-}\phi$, $e^{g\phi}$, $e^{2g\phi}$ are constructed consistently in terms of the free field. The Liouville model field theory space is found to be restricted to the sector with field momentum $P_{+}=-P_{-}$, $P_{+}> 0$ , which is a closed subspace for the Liouville theory operator algebra.Comment: 16 p, EFI-92-6

On Nonperturbative Calculations in Quantum Electrodynamics

A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach allows one to take into account the gauge invariance conditions (Ward identities) and to perform the renormalization program. The iteration scheme can be realized in two versions. The first one ("perturbative vacuum") corresponds to chain summation in the diagram language. In this version in four-dimensional theory the non-physical singularity (Landau pole) arises which leads to the triviality of the renormalized theory. The second version ("nonperturbative vacuum") corresponds to ladder summation and permits one to make non-perturbative calculations of physical quantities in spite of the triviality problem. For chiral-symmetrical leading approximation two terms of the expansion of the first-step vertex function over photon momentum are calculated. A formula for anomalous magnetic moment is obtained. A problem of dynamical chiral symmetry breaking (DCSB) is considered, the calculations are performed for renormalized theory in Minkowsky space. In the strong coupling region DCSB-solutions arise. For the renormalized theory a DCSB-solution is also possible in the weak coupling region but with a subsidiary condition on the value of $\alpha$.Comment: 31 pages, Plain LaTex, no figures. Journal version: some discussion and refs. are adde

One-Dimensional and Multi-Dimensional Integral Transforms of Buschman–Erdélyi Type with Legendre Functions in Kernels

This paper consists of two parts. In the first part we give a brief survey of results on Buschman–Erdélyi operators, which are transmutations for the Bessel singular operator. Main properties and applications of Buschman–Erdélyi operators are outlined. In the second part of the paper we consider multi-dimensional integral transforms of Buschman–Erdélyi type with Legendre functions in kernels. Complete proofs are given in this part, main tools are based on Mellin transform properties and usage of Fox H-functions

Absorption of Gamma-Ray Photons in a Vacuum Neutron Star Magnetosphere: I. Electron-Positron Pair Production

The production of electron-positron pairs in a vacuum neutron star magnetosphere is investigated for both low (compared to the Schwinger one) and high magnetic fields. The case of a strong longitudinal electric field where the produced electrons and positrons acquire a stationary Lorentz factor in a short time is considered. The source of electron-positron pairs has been calculated with allowance made for the pair production by curvature and synchrotron photons. Synchrotron photons are shown to make a major contribution to the total pair production rate in a weak magnetic field. At the same time, the contribution from bremsstrahlung photons may be neglected. The existence of a time delay due to the finiteness of the electron and positron acceleration time leads to a great reduction in the electron-positron plasma generation rate compared to the case of a zero time delay. The effective local source of electron-positron pairs has been constructed. It can be used in the hydrodynamic equations that describe the development of a cascade after the absorption of a photon from the cosmic gamma-ray background in a neutron star magnetosphere.Comment: 29 pages, 1 figur