L. De Falco

Unitary and pseudounitary symmetries in a generalized statistics

Abstract We show that the “guonic” formalism, based on a g - operator deformation of the Heisenberg-Weyl algebra, preserves, under a Jordan-Schwinger map, unitary (U(N)) and pseudounitary (SU(1,1)) symmetries. This result is a strict consequence of the properties of the operator g .

New classification of particles statistics

SummaryWe propose a new classification of particles statistics by means of the recently proposed operatorial generalization of the Fermi and Bose statistics, by which it is possible to distinguish between intrinsically and non-intrinsically defined statistics.

Variational approach to generalized statistics

SummaryBy means of the Schwinger variational, principle, we show that a field theory with a linearly realized symmetry admits the generalizedg-statistics as a possible solution.

q-parameter dependence of a gas in equilibrium with a deformed solid

Abstract We show that the main thermodynamical quantities of a gas in equilibrium with a deformed solid (composed by q-oscillators) exhibit a dependence on the deformation parameter of the lattice oscillators.

Bosonic and fermionic realizations of an operator-deformed Heisenberg-Weyl algebra

SummaryStarting from independent sets of one-dimensional «bosonic» and «fermionic» operators, we build up both a «bosonic» and a «fermionic» even-dimensional realization of an operatorial deformation of the Heisenberg-Weyl algebra, recently introduced to describe particles with intermediate statistics (guons). It is shown that these two deformed algebras are connected by unitary transformation. Mixed realizations are also generated by a simple change of representation.

Approximation Method for the Partition Function of an Anharmonic-Oscillator Gas

We use an approximation procedure to find the partition function of a gas composed by anharmonic oscillators in a region where perturbation theory breaks down. The results are still quite accurate for small values of the coupling constant.

Approximation method for the density matrix of an anharmonic-oscillator gas

Abstract We use an optimization method to find the closest approximation to the density matrix of a gas composed of anharmonic oscillators for such values of the coupling constant that perturbation theory breaks down.

Harmonic oscillator with generalized statistics

SummaryUsing the formalism ofg-operator we find a generalization of the harmonic-oscillator algebra, which contains as particular cases the boson and fermion oscillators. The form of the creation and annihilation operators is obtained as a function of two operators, α and β, which satisfy a certain new algebra of the Lie-admissible type.

An alternative approach to deformed statistics

SummaryStarting from general assumptions about creation and annihilation operators we propose a new generalized approach to deformed statistics, which permits to distinguish between two different situations; the first, in which we may define an intrinsically defined statistics, and the second one, in which this is not possible, because the symmetry properties of the system are determined by the vacuum state. The dynamical evolution of the generalized particles (guons) is derived by exploiting the Lie-admissible structure of theg-algebra.