abstract

A gravitational theory based on the generalised affine geometry is presented. It contains an antisymmetric torsion potential in addition to the metric. The coupling to matter is derived by the minimal coupling principle, implying that the metric couples to a symmetrised energy-momentum tensor, and the antisymmetric field couples to the canonical spin tensor of matter. The coupling constant for both cases is Newton’s constant, \(G\). Phenomenological consequences of the linearised theory for quantum processes at the tree level are explored.

abstract

The Kepler problem in the Lobachevsky space is solved.

abstract

We continue our investigation of formation of trapped surfaces in strongly curved geometries which do not contain gravitational waves. The expansion of open, flat universes does not change substantially the results obtained hitherto in the case of asymptotically and conformally flat space-time. The necessary and sufficient conditions for the formation of trapped surfaces are given, which explicitly demonstrate that the quicker universes are expanding, the more matter is required to develop a trapped surface.

abstract

We present the leading logarithmic third order, \(\mathcal {O}(\beta ^3)\), corrections to the electron structure functions in QED. For the non singlet component we present exact Monte Carlo algorithm and compare several approximate (exponentiated) solutions. Using structure functions we discuss the QED initial state photonic (i.e. without additional fermion pairs) corrections to total cross-section at LEP. We find the size of \(\mathcal {O}(\beta ^3)\) corrections, in the range \(|\sqrt {s}-M_Z| \leq 2.5\) GeV, to be \(\Delta \sigma ^{(3)}/\sigma \leq 0.12\)% for Kuraev–Fadin and \(\leq 0.01\)% for Jadach–Ward ad hoc exponentiated formulas, respectively. We show that in the case of the exponentiated formulas the stronger cuts more efficiently eliminate higher order corrections. Finally, we propose a new, compact, “pragmatic”, i.e. without numerically unimportant subleading terms, \(\mathcal {O}(\alpha ^3)\) formula for the initial state QED photonic part of the total cross-section at LEP, accurate to \(\delta \sigma /\sigma \leq 0.015\)% for \(|\sqrt {s}-M_Z| \leq 2.5\) GeV and 0.035% for \(|\sqrt {s}-M_Z| \leq 7.5\) GeV.