Past Research Activity of Stefano Ansoldi

My research background and interests are mainly in the area of quantum gravity.

 

The difficulties encountered in the process of developing such a theory can be summarized in the difficulties of having a theoretical description of both, large scale and small scale phenomena. Extended objects (string, branes (shells)) can be of help for this problem. In particular, in the past I worked on the study of the dynamics of extended objects from two different perspectives:

  1. developing the theory of extended objects in a formulation a la Eguchi;
  2. studying the semiclassical quantization of extended objects in general
    relativity.

 

In the first case, a great advantage of Eguchi's formulation of string dynamics is that it treats the extended object as a whole dynamical entity, without focusing on its constituents (points). The motion of the object can then be described in what is called loop space. In particular we worked on giving a path-integral formulation of string dynamics a la Eguchi [2], showing that the quantum dynamics can be described in terms of fractal properties of the world-sheet [6] and interpreting in terms of these aspects the small-scale space-time structure, whose microscopic constituents are branes, instead of points [7].

This work has been complemented by more technical results, about the required mathematical framework and its relations with more standard approaches [8,12]. As applications, the duality properties of this formulation [9,11] and possible applications to the vacuum structure [3], dark matter [16] and to QCD [14,18] have also been considered. Additional results have been obtained in connection with the formulation of an uncertainty principle for p-branes [19], with the relation between strings and Yang-Mills theories [15,20] and with the propagator of p-branes in a suitable quenched minisuperspace approximation [17].

It is also interesting to note that some results from the functional formulation of extended objects dynamics can be used to reinterpret the path integral approach to the derivation of the particle propagator in non-relativistic quantum mechanics [10].

 

In more recent years I have been coming back to the study of extended objects in general relativity, which has been my preoccupation since the days of the Laurea thesis [4,5] (see also [13] for a heuristic approach that tries to put together relativistic causality and uncertainty principle). In particular, already at that time a Lagrangian description of Israel junction's conditions in spherical symmetry was developed. It is just a re-formulation of some results already present in the literature.

The interest in shells, at the time, was in connection with a description of vacuum bubbles nucleation, and applications to phase transitions in the early universe and to the initial singularity problem. Some of these problems were tackled in the literature with ad hoc conditions or assumptions, different from work to work, and the goal was simply to reproduce those results in a Lagrangian framework, with little effort and a routine work computation.

Not only this turned out to be possible [5]: the same framework can also be used, with little modifications, to study a different problem, i.e. the determination of the quantum states of a shell when its action is of the order of the Planck constant, i.e. when the shell is in a quantum regime. In a particular case I could determine the quantum states of the shell, a genuinely general relativistic system, in the semiclassical approximation [21].

Now this promising analysis needs to be generalized to more complex situations. Since shells have already been useful models of many gravitational systems, in their classical regime, it is my hope that a quantum study at or beyond the semiclassical level, will give an insight into some aspects of quantum gravity. In particular, as a long-term research perspective, I would like to find an application to gravitational entropy and black hole thermodynamics, maybe in terms of an information theoretical approach to the dynamics of the shell.
Stefano Ansoldi