Spherically symmetric collapse in quantum gravity

The problem of classical singularities is revised on the basis of the quantum-gravity effective equations. We find a simple rule for establishing the Birkhoff theorem in spherically symmetric problems. All exact solutions of the lagrangian with C²_αβγσ are obtained. Spherically symmetric collapse of the thin null shell of mass M is considered in the framework of a local theory describing vacuum polarization effects. The boundary-value problem is set and the asymptotic solution is obtained. It is found that the shell collapses to r = 0 without the rise of a singularity, and begins expanding. The global behaviour of the solution is obtained for small M. For large M it is conjectured that the event horizon does not form, and the apparent horizon is closed. An object forms, possessing the observable properties of a black hole, but living a finite time.     

Magnetic charge,black holes,and cosmic censorship

The possibility of converting a Reissner-Nordström black hole into a naked singularity by means of test particle accretion is considered. The dually charged Reissner-Nordström metric describes a black hole only when M² > Q³ + P². The test particle equations of motion are shown to allow test particles with arbitrarily large magnetic charge/mass ratios to fall radially into electrically charged black holes. To determine the nature of the final state (black hole or naked singularity) an exact solution of Einstein's equations representing a spherical shell of magnetically charged dust falling into an electrically charged black hole is studied. Naked singularities are never formed so long as the weak energy condition is obeyed by the infalling matter. The differences between the spherical shell model and an infalling point test particle are examined and discussed.     

Three-body scattering in configuration space

The asymptotic forms of the wavefunction and Faddeev components in configuration space are shown to determine uniquely the solutions of the Schrödinger or Faddeev differential equations for 2 → (2, 3) and 3 → (2, 3) processes. An antisymmetrized form of the Faddeev differential equation for three equivalent fermions is given and its angular analysis is performed in the general case of local potentials with tensor interaction for neutron-deuteron scattering. We describe a numerical method for solving the corresponding boundary value problem and apply it to scattering and break-up at E_n^1ab = 14.4 MeV in the doublet S state for the four local potentials of Malfliet and Tjon, Reid, de Tourreil and Sprung, and de Tourreil, Rouben and Sprung. For the three realistic potentials, elastic scattering amplitudes differ by 5%, and amplitudes for break-up in the two-neutron state ¹S₀ differ by less than 4%.     

Calculation of theO(α s 2 ) parity-violating structure functions ine^ + e^ - \to q\bar qg

We calculate the two nonvanishingO(α _s ² ) parity-violating structure functions that contribute to \(e^ + e^ - \xrightarrow{{\gamma ,Z}}q\bar qg\) . We discuss how these can be measured. We work with massless quarks and gluons and use dimensional regularization to regularize ultra-violet and infrared singularities. We carefully discuss how to deal withγ ₅ in the dimensional regularization scheme when infrared singularities are present.     

Relativistic three-quark equations and mass spectrum of the (70, 1<Superscript>−</Superscript>) baryon multiplet

A relativistic generalization of three-quark Faddeev equations for the particles of the (70, 1^?) multiplet is constructed within the dispersion-relation approach. An approximate solution to the relativistic three-quark equations is obtained on the basis of the method of isolating leading singularities of scattering amplitudes. The mass spectrum of the (70, 1^?) multiplet is calculated, and the result is in rather good agreement with corresponding experimental data.     

Infrared singularities in the dimensional regularization scheme

Infrared singularities arising in some renormalized amplitudes of quantum electrodynamics are analyzed using the dimensional regularization method. We define infrared and ultraviolet convergent regions in the ν complex plane (ν is the number of dimensions of space time). It turns out that these regions do not overlap for quantum electrodynamics. Nevertheless, it is shown that there exists a unique analytic continuation from the infrared convergent region which allows us to interpret the infrared divergence in the renormalized electron self-energy amplitude as an isolated singularity at ν = 4. This statement seems to be true at all orders of perturbation theory. We also prove that the double limit μ → 0, ν → 4 (μ is the auxiliary photon mass) does not exist in quantum electrodynamics and we conjecture that this lack of uniformity provides theoretical support for the ansatz of Marciano and Sirlin.     

How to regularize the infrared and mass singularities in QCD

The parton cross sections in perturbative QCD are mass (M) and infrared (IR) divergent. The singularities are prevented by on/off-shell parton masses or by dimensional regularization. All mass assignments must be chosen in agreement with Kinoshita's double-cut rule. The “off-shell” assignment, often used in the past, is incorrect. We demonstrate that Drell-Yan mass factorization in order α_S is independent of all regularizatiohns; the coffcient function is unique.     

<Emphasis Type="Italic">J</Emphasis><Subscript><Emphasis Type="Italic">AW,WA</Emphasis></Subscript> functions in Passarino-Veltman reduction

We continue to study a special class of Passarino-Veltman functions J arising at the reduction of infrared divergent box diagrams. We describe a procedure of separation of two types of singularities, infrared and mass singularities, which are absorbed in simple C ₀ functions. The infrared divergences of C ₀’s can be regularized then by any method: photon mass, dimensionally or by the width of an unstable particle. Functions D ₀ are represented as certain linear combinations of the standard C ₀ Passarino-Veltman functions and infrared finite functions J. Then mass singularities are extracted from J to other combinations of C ₀. The rests are free of both types of singularities and are expressed as explicit and compact linear combination of logarithms and dilogarithm functions. The extensive comparison of numerical results with those obtained with the aid of the Loop Tools package is presented.     

Cosmological singularities and higher-order gravitational lagrangians

General relativity is modified by adding terms proportional to R² and R^μνR_μν to the Lagrangian. One class of solutions of the modified field equations is free of singularities but does not lead to asymptotic behaviour (for large time) of the Friedmann type. A second class, which shows the correct asymptotic behaviour, does contain the usual singularities of Friedmann universes, collapse being modulated by small oscillations only. The quantum effects considered here are thus unable to prevent the occurrence of cosmological singularities under physically reasonable conditions.     

Geometrical description of binary reactions and large p⊥ phenomena

We study consequences of defining the impact parameter as being the variable conjugate to transverse relative c.m. momentum, p_⊥. This coincides with a proposal originally made by Chang and Raman. The dynamical information carried by these are intimately connected to the behaviour of 90° scattering. In particular, impact parameter dynamics is a priori qualitatively different from direct channel angular momentum dynamics. A phenomenological study of elastic π^±p and pp data at fixed values of longitudinal momentum, p₆, leads to a generalized geometrical scaling hypothesis. In contrast with the power behaviour predicted by parton models, the data suggest exponential behaviour of the scaling amplitudes at fixed p₆ of the type e^Rp⊥ with R ? 1 fm. Correspondingly these amplitudes are described by a pair of complex conjugate singularities on the imaginary axis in the impact parameter plane.     

The calculation of critical amplitudes in SU(2) lattice gauge theory

We calculate the critical amplitudes of the Polyakov loop and its susceptibility at the deconfinement transition of (3 + 1)-dimensional SU(2) gauge theory. To this end we study the corrections due to irrelevant exponents in the scaling functions. As a guiding line for determining the critical amplitudes we use envelope equations which we derive from the finite size scaling formulae of the observables. We have produced new high precision data on N_{σ³ × 4} lattices for N_χ = 12, 18, 26 and 36. With these data we find different corrections to the asymptotic scaling behaviour above and below the transition. Our result for the universal ratio of the susceptibility amplitudes is C₊/C₋ = 4.72(11) and thus in excellent agreement with a recent measurement for the 3d Ising model.     

Reciprocal space-time and momentum-space singularities in the narrow resonance approximation

A general scheme is proposed which makes explicit the relationship between the singularities of off-shell amplitudes in position-space and momentum-space in the narrow resonnace approximation. In some ways this may be viewed as a duality scheme for amplitudes involving external quarks, in which narrow resonances in certain channels build the Fourier transform of power singularities in x² (x^μ being a position vector). This scheme is made precise by dual string off-shell amplitudes. As well as highlighting possible connections between the general dual framework and the structure of confined field theories we are able to pinpoint certain grave shortcomings of present dual models.     

Reggeized symmetry models and pion-nucleon scattering in forward and backward directions

A Reggeization procedure is developed for higher symmetry schemes and its relationship with the SU(6) × SU(6) Reggeization is exhibited. The kinematic singularities arising from SU(6)_W-invariant vertex functions are removed with the help of fixed cuts and the resulting scattering amplitudes are extrapolated to hadron poles. The essentially parameter free theory thus obtained is shown to lead to reasonable forward and backward differential cross sections in pion-nucleon scattering at high energies.     

J A functions in the Passarino-Veltman reduction

In this paper we consider a special class of Passarino-Veltman functions which appear during the reduction of the box-type diagrams with infrared divergences and mass singularities. A systematic procedure has been proposed to separate both types of singularities into sthe simplest objects: C ₀ functions. New J _A functions are certain linear combinations of the standard D ₀ and C ₀ functions, which are free from all types of singularities, and they have a compact expression in terms of logarithms and dilogarithms. Our results have been numerically compared with the calculations using the well-known package LoopTools.     

Ambiguities in the infrared regularization of QCD

The next-to-leading corrections of leading-log asymptotic freedom are determined in the known infrared (IR) regularization schemes. On- and off-shell calculation leads to different answers; the n-dimensional regularization of IR and mass singularities agrees with the on-shell results. The non-log corrections in Drell-Yan processes are important for Q² ? 10³ GeV².     

G2-Monopoles with Singularities (Examples)

G₂-Monopoles are solutions to gauge theoretical equations on G₂-manifolds. If the G₂-manifolds under consideration are compact, then any irreducible G₂-monopole must have singularities. It is then important to understand which kind of singularities G₂-monopoles can have. We give examples (in the noncompact case) of non-Abelian monopoles with Dirac type singularities, and examples of monopoles whose singularities are not of that type. We also give an existence result for Abelian monopoles with Dirac type singularities on compact manifolds. This should be one of the building blocks in a gluing construction aimed at constructing non-Abelian ones.     

Infrared and mass singularities cancellation in finite-temperature and -density radiative corrections to the MSW effect

Finite-temperature and -density radiative corrections to orderα to the charged-current MSW process are considered in the real-time version of thermal field theory. We confirm the absence of infrared and electron mass singularities in the real part of thev _e self-energy, calculated in a background of electrons at finite chemical potential. As a consequence, this indicates that at orderα the perturbation series with respect to electromagnetic interactions is adequate for a coherent process.