Table of contents

N=4 SU(2) conformal invariance is studied in harmonic superspace. The superconformal structure is solved by harmonic analyticity. Conformal tensors are primary analytic superfields Phi ^q completely specified by the Cartan-Weyl charge q. The conformal weight h is equal to q/2. The super-Schwarzian derivative is calculated and the infinitesimal anomaly-free transformations are discussed. It is shown that all conformal degrees of freedom are carried by variation of the harmonics.

Implicitly contained in recent results of Dray and Joshi (1990) is the possibility of joining Reissner-Nordstrom spacetimes with different charges and masses along colliding charged shells in such a way that there is no mass or charge associated with two of the 'shells'. These results can be used to model at collapsing charged shell which bounces when its total (gravitational and electromagnetic) energy is zero and also to model the spontaneous creation of particle/antiparticle pairs.

The author shows that a spacetime for which the matter content is pure (null) shear-free and twisting radiation, with or without a cosmological constant cannot admit a proper conformal Killing vector field.

It is shown that all theories involving a real scalar field or an electromagnetic field nonminimally coupled to Einstein gravity in four dimensions, are actually 'pseudogravitational nonminimally coupled theories', since they do not violate the weak equivalence principle. Furthermore, one can totally eliminate the appearance of the gravitational field in the equations of motion concerning the matter fields which couple with gravity.

The authors re-examine the problem of spontaneously broken gauge theories in curved spacetime. They show that introducing a nonminimal coupling of the scalar field with gravity opens the possibility of inducing spontaneous symmetry breaking without the need to choose a negative value for m². Using this idea in the framework of a grand unified model, they calculate the Higgs mass, the value of the cosmological constant and the effective gravitational constant.

The authors perform a semiclassical expansion in the Wheeler-DeWitt equation, in powers of the gravitational constant. They then show that quantum gravitational fluctuations can provide a correction to the wavefunctions which are solutions of the Schrodinger equation for matter. This also implies a correction to the expectation values of quantum mechanical observables.

The simple formulae for a number of massless particles created in anisotropic spacetime are derived. The physical interpretation of the effect is given.

The authors connect the number of elementary particle generations, in the context of grand unified theories (GUT) based on a gauge group G, with the number of principal fibre bundles representing fundamental monopoles. These are in 1:1 correspondence with the invariant subgroups of the cohomology group H^k+1 (B:A) of the base B and with coefficients in the first non-trivial homotopy group, Pi _k(G)=A, of the structural group having the same Lie algebra G as the gauge group G.

The Kaluza-Klein reduction of a generalised theory of gravity in D=5 dimensions is given. The form of the interactions among the gravitational, electromagnetic and massless scalar fields in four dimensional spacetime is exhibited.

Spacetimes which represent the interaction of two plane asymptotic waves are defined, and shown to be a more realistic generalisation of colliding plane waves. For the case of collinear polarisation, general asymptotic waves, restricted by the criterion that they have bounded amplitudes at their caustics, generically produce an unavoidable curvature singularity. The results are first illustrated by a class of exact solutions. The methods used apply equally to colliding plane waves.

The Hawking effect is investigated on a classical model spacetime (the Vaidya-Bonnor linear spacetime), which represents a dynamically evaporating charged black hole. Under the two-dimensional approximation, the expectation value is calculated of the stress-energy tensor of a massless scalar field with respect to the generalised Unruh vacuum. The obtained vacuum expectation value diverges on the Cauchy and anti-Cauchy horizons of the model spacetime. This suggests that these horizons are quantum theoretically unstable.

Power-law inflation is shown to be a local attractor for t to infinity in the space of inhomogeneous solutions of the Einstein theory of gravity with a minimally coupled scalar field having a positive exponential potential. Applying the conformal equivalence theorem the authors show that a similar result holds true for fourth-order gravity with the Lagrangian L=R^M, M not=, 1, 2.

The mathematical principles underlying the theory of gauge-invariant perturbations of homogeneous isotropic cosmological models are discussed and a collection of useful formulae is given.

Actions containing R² terms in D=4, N=1 supergravity are constructed in the on-shell and the new minimal formulation of the theory. The basic feature in both cases is an analogy between supersymmetric Yang-Mills theory and supergravity. This analogy is also used to construct supersymmetric Lorentz Chern-Simons terms, which allows a derivation in D=4 of an effective action resulting from string compactification.

The renormalisation structure of gauge models in curved spacetime with torsion is considered. For Abelian theory the classical action, leading to multiplicatively renormalised theory, is constructed. The multiplicativity of renormalisation requires nonminimal coupling of a vector Abelian field with torsion. The authors investigate the renormalisation group equations for effective nonminimal coupling constants in nonAbelian theory. They find that the equations for essential nonminimal couplings have the universal structure. Due to radiative corrections the interaction between spinor fields and torsion become more intense in the strong gravitational field.

The authors enlarge the SU (1,1) group (metric, connection, and Hamiltonian) of the elementary affine model of gravity by the U(1) phase invariance of quantum mechanics. The quantum dynamics can be obtained from the enlarged group (SU(1,1) (X) U(1)). They also obtain a correction of the classical Hamiltonian which makes it the generator of the compact subgroup of SU(1, 1). The quantum wavefunctions are explicitly worked out in both the coherent state and metric diagonal representation. It is proved that they carry the unitary discrete representations of SU (1, 1) and respect the positivity requirement of the quantum metric operator. They also present a generalisation of the model and discuss further applications to quantum gravity.

The authors show that the spontaneous compactification in M⁴*CP² is possible with instantons defined on CP². By coupling the U(1) instanton with fermions and using index theorem arguments it is shown that one can possibly define chiral fermions consistently.

Statistical estimates of thermal fluctuations of a torsion pendulum used to detect weak forces are re-examined by a more general approach with special reference to gravitational experiments. Thermal limitations on the measurement of the displacement of a pendulum and on the measurement of its period are both studied. In the study of the uncertainty of displacement due to thermal noise it is found that the effect has been underestimated in some experiments on gravitation if the displacement is measured in a discrete way; it is also found that a continuous measurement of the displacement in a non-equilibrium state of a pendulum can depress the thermal noise level greatly; in some special cases it can reduce it by nearly a factor of Q and the formula of Braginsky (1977) and others is re-interpreted. In the study of the uncertainty of the period due to thermal noise, it is found that there is an optimum measurement time for which the uncertainty due to thermal noise in the measurement of the period is a minimum.

Explicit formulae are presented for the connection, curvature and Ricci tensor on the diffeomorphism group SDiffS³. The structure constants for SDiffS² are given in closed form and some known results rederived.

In Kaluza-Klein theory it is known that the dimensional reduction induced by an n-dimensional (non-Abelian) isometry group G is consistent with (4+n)-dimensional general covariance. With the isometry group as the fibre it is shown that the scalar sector of the theory defined by the Einstein-Cartan-Hilbert action in (4+n) dimensions can drive a successful inflation in a cosmological setting, if one identifies the conformally transformed metric as the new physical spacetime metric and assumes non-vanishing torsional bilinears. The vacuum, which has vanishing gauge and scalar fields, is found to be a four-dimensional Minkowski space with the Cartan-Killing metric on the group space for a compact group G.

The authors quantize the Abelian and nonAbelian Chern-Simons theories in (2+1) dimensions by the Dirac quantization formulation. Gauge theories with a topological mass term in both the Abelian and nonAbelian cases are also quantized by the same method.