Roberto Cianci

Structure of supermanifolds and supersymmetry transformations

After giving a global, constraint-free Lagrangian formulation of theN=1 superspace supergravity in terms of super fibre bundles and differential forms over a supermanifold, we show that the concept of body manifold of a supermanifold provides a natural manner to reduce the theory to spacetime. This reduction, however, is not canonical, and the various ways in which it can be done give rise to transformations of the field variables which generalise the known invariances of theN=1 spacetime supergravity under supersymmetry transformations and spacetime diffeomorphisms.

An existence result for super Lie groups

An analogue of the classical global third Lie theorem is proved to hold for super Lie groups whose ground Banach—Grassmann algebra is (possibly) infinite-dimensional, provided that this algebra has an ordered basis. It is also proved that the superanalytic structure of a connected super Lie group having a prescribed Lie module is unique, although in a weaker sense than in the case of ordinary Lie groups.

On the structure of superfields in a field theory on a supermanifold

In view of applications to the formulation of gauge field theories on supermanifolds, we study the relation between the sheaves of functions on a supermanifold M and its body manifold M0, respectively. The nonuniqueness of the local injections t: M0→M is analysed in consideration of its role in supersymmetric field theories. A Banach space structure is given to the set of bounded, supersmooth, Ckfields on M in order to get a rigorous formulation of variational principles for the class of theories under consideration.

Generalized axisymmetric spacetimes

Properties of space-times admitting a two parameter abelian symmetry group acting on a null two-surface are investigated. Within this framework, a class of new solutions of Einsteins vacuum equations are found. Some analogies with the theory of black hole are pointed out.

Comments on limits of space-times

A coordinate-dependent investigation of limits of space-times is given. Different kinds of limits are found and analyzed. A criterion selecting limits which appear to be nothing but “technical tricks” is proposed. Finally, a method for generating new limits from a given family of metrics is examined.

Reduced fiber bundles and symmetries of gauge field theories rigid reductions and the einstein-cartan theory

The process of the reduction of a principal fibre bundle P(M, G) to a reduced subbundle Q(M, H) is analysed in view of applications to the description of symmetries of gauge theories. The main idea is to relate symmetries of the nonuniqueness of the reduction by gauging the different ways in which for each fiber the unbroken group H is imbedded into the large group G. Gauge theories encompassing gravitation are especially taken into account.

On generalized torsion two-forms in general relativity: a result of null tetrad formalism

The method of reduction of a connection form from a principal fibre-bundle to a sub-bundle is studied by considering the null tetrad formalism in space-time and discussing in detail the resulting Generalized Maurer-Cartan Structural Equations.Vacuum space-times satisfying Einstein field equations and admitting the vanishing of the induced curvature form in the reduced bundle are investigated. It is shown that these hypotheses imply the existence of a field surface orthogonal to a real null geodesic vector of the tetrad field.