Table of contents

In three spacetime dimensions, the coupled massless spin-5/2-Einstein system exhibits a new local supersymmetry parametrised by a vector-spinor rather than a spinor as in supergravity. Although the theory does not contain dynamics, but only torsion, this hypersymmetry still formally ensures consistency. The analysis extends to arbitrary rank fermions.

An alternative formulation for massless fields with half-integer spin is given, using vector -((j-1,0)(+)(0,j-1)) spinor fields. The simple Abelian gauge invariance of the (nonlinear) field equation is demonstrated, and the non-minimality of the resulting coupling with gravity is briefly discussed.

The free gravitino field is formulated in the continuum in terms of cross-sections of a Kahler-Atiyah bundle. This leads naturally to a lattice formulation for free gravitinos with local supersymmetry but no spectrum doubling in the dispersion relation.

The authors formulate a CPT theorem for Minkowski space-times of any dimension; there is a distinction between the even- and odd-dimensional cases. Moreover, in odd dimensions fermion mass terms violate either C or T, and always violate P. They also discuss the appearance of CP violation in Kaluza-Klein model with massive fermions.

A revised model of the inflationary universe under the framework of Brans-Dicke theory is proposed. It is shown that the scale factor of the universe during the inflation varies as R approximately t^w+1/2 and not exponentially, but still it gives rise to enough inflation to solve the cosmological puzzles. It is found that the quantum gravity effects come into play in the same scale as that of grand unified theories (i.e. at T approximately 10¹⁴ GeV) rather than at T approximately 10¹⁹ GeV, hence providing a natural solution to the 'milder version' of the flatness problem inherent in the conventional inflationary scenarios. This scenario also provides a simple way to estimate theoretically the present value of the gravitational constant. The estimated value agrees well with the actual value despite many approximations and the ignorance of quantum gravity; the difference is only by a factor of the order of 10^-2.

Using the framework of affine differential geometry, which is related to the gauge theory of the Poincare group, the author discusses the geometric interpretation of the non-symmetric field structure originally proposed by Einstein and Straus (1946).

It has been suggested that the Poincare group be gauged through the introduction of connections on Poincare sub-bundles of the bundle of affine frames over space-time, and that such constructions lead to the so-called Riemann-Cartan space-times. The author gives a detailed presentation of this approach, including a complete characterisation of the affine vertical automorphisms which arise in the course of the argument. The discussion does not rely on reductions of the affine frame bundle to the linear frame bundle.

A limiting procedure is applied to construct nongauge solutions to the linearised spin-3/2 field in N=1 supergravity. The background metric represents a gravitational pp-wave arising from boosting the Schwarzschild line element to the speed of light, while the gravitino field is the induced limit of a pure gauge solution on the Schwarzschild background.

A Euclidean quantum conformal gravity in a linear approximation is considered. It is assumed that its solution possesses an exact conformal symmetry. The main difficulty, which is a characteristic not only of gravitation theory but of all gauge theories as well, consists in the fact that in all previous formulations the conformal invariance can be stated unambiguously only in the purely gauge sector. In the present new formulation this difficulty is absent. This is obtained by means of new transformation laws for the metric tensor field h_{mu nu} and energy-momentum tensor T_{mu nu} . Previous transformation laws corresponded to the indecomposable representations of the conformal group and this fact was the origin of the difficulty mentioned. Explicit expressions are obtained for the propagator of the field h_{mu nu} as well as for the three-point functions including h_{mu nu} or T_{mu nu} and the matter fields. It is shown that the equations of linear conformal gravity are the consequences of the conformal invariance. They are the manifestation of a mathematical fact of the equivalence of the conformal group representations attributed in the approach to the fields h_{mu nu} , T_{mu nu} and the Weyl tensor.

A recent approach to quantum gravity leading to the concept of quantum stationary geometries is reviewed. A stationary states equation is presented for: (a) homogeneous relativistic cosmologies of the various Bianchi types; (b) a Friedmann universe filled with a massless scalar field. The equation is solved near the singularity to show that stationary states avoid the singularity. The result is discussed and compared with other approaches.

The authors discuss a linear approximation of the nonsymmetric Kaluza-Klein theory. They find the electromagnetic and Yang-Mills field Lagrangians up to the second order of approximation in h_{mu nu} =g_{mu nu} - eta _{mu nu} . They prove that in the electromagnetic case there is no skewon-photon interaction up to the first order of approximation.

The modification of the inhomogeneous metric due to trace anomaly has been analysed. The behaviour of the perturbed energy density seems to suggest the homogenisation effect of the original spacetime.

The authors study the response of a uniformly accelerated model particle detector in a spacetime with compact spatial sections. The basic thermal character of the response re-emerges, in spite of the fact that the spacetime does not possess event horizons. The model also permits a study of detector response to twisted field states.

For pt.III see J. Phys.A. vol.15, p.1057 (1982). Sets of massive spin-3/2 and spin-2 equations are known which are internally consistent in an arbitrary Riemann space. Each such set may be split up into a symmetric part (the 'field equations') and a skew-symmetric part (the 'subsidiary conditions'). Lagrangians are now constructed which generate the field equations, granted that the subsidiary conditions are imposed after variation.

Solutions of the stationary axisymmetric Einstein-Maxwell electrovac equations are presented, for which the metric is a function of the radial coordinate r only, while the electromagnetic potentials also depend on the z coordinate. These solutions are shown to follow from the Ernst potentials Phi =F(r)e^iqz and G=f(r)-F²+icz, up to a duality rotation.

The problem of a cylindrically symmetric configuration of charged rotating dust is studied under the additional assumption that the Lorentz force on a typical particle of the fluid vanishes. Exact solutions with differential rotation are presented both in Newtonian physics and in general relativity. In the Newtonian case one particular solution exists which is regular, but which has a vanishing matter density on the axis. For the relativistic case the general solutions of the problem can be given in terms of hypergeometric functions; particular families of solutions are discussed for which the relevant physical quantities are regular on the axis.