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In this paper we exploit the Schrodinger factorization technique, in its modern supersymmetric version, to propose a variational method for excited states of one-dimensional systems.

In this paper we develop the notion of adiabatic holonomy in {ital classical} fermionic field theory and apply it to chiral gauge theory. In chiral gauge theory the {ital classical} adiabatic holonomy leads to a deformation of the Poisson algebra of translation generators in the space of gauge fields and to an additional term in the Poisson brackets among gauge-transformation generators. We study all this in detail in a (1+1)-dimensional model.

The authors present a thorough analysis of the removability of the Berry phase. They show that for any system they can, by properly restricting the parameter space turn the geometrical phase into an extra shift of the dynamical one. However, this extra shift in the dynamical phase retains its truly geometrical character. The removability is thus only apparent and the geometrical phase can still be measured in interference experiments, as indeed has already been done several times.

In this paper we introduce some mathematical tools to further study the classical adiabatic holo- nomy effect known as Hannay's angle. In particular, we prove with purely classical methods that the area (or angle) two-form associated with this effect can be seen as a modification of the symplectic structure of the slow-variable dynamics. We also show that, as in the quantum case, degeneracies cause singularities in this two-form. We conclude with some considerations concerning the triviality or nontriviality of the phase-space bundle associated with this phenomenon.

The ``geometrical phase factor,'' found by Berry in his study of the quantum adiabatic theorem, has a classical analogue discovered recently by Hannay and Berry himself. This classical analogue consists of an extra angle swept by the system in its classical evolution during an adiabatic excursion. As in Berry's phase, Hannay's angle reflects a nontrivial holonomy of the system and it has a purely geometric character. In this paper we calculate Hannay's angles for the classical Grassmannian system associated to a quantum spin in a magnetic field. We also show their close relation to the corresponding quantum-mechanical phase of Berry for the same system.