Toward a metric description of hadronic interaction from Bose-Einstein correlation

We discuss the problem of second-order correlation in pion production in high-energy processes (commonly known as Bose-Einstein correlation) by means of the concept of nonlocality and its mathematical realization via the isotopy of Hilbert and Minkowski spaces. Such a nonlocal approach allows one to describe the spatial shape of the source when: pions are produced (<<fireball>>), and to account also for the correlation in phase. The correlation function obtained by this method does not contain free <<ad hoc>> parameters. Moreover, the test of this nonlocal correlation function, performed an the UA1 experimental data, is as good as that given by the conventional treatment. Such an approach suggests an interpretation of the pion production as a decay process of the fireball, whose <<meanlife>> is explicitly evaluated. Using the data of the UA1 ramping run, we find the expression of the metric parameters as functions of the energy. They provide an effective dynamical description of the hadronic interaction in terms of a deformation of the Minkowski metric. The related parameters of the fireball admit of future experimental verification at DELPHI. The law of deformation of time in presence of a hadronic field is derived. Its behaviour with the energy allows one to give an appealing picture of confinement and asymptotic freedom of hadronic constituents.