Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.

A NOTE ON GAUSSIAN INTEGRALS OVER PARA-GRASSMANN VARIABLES

We discuss the generalization of the connection between the determinant of an operator entering a quadratic form and the associated Gaussian path-integral valid for Grassmann variables to the para-Grassmann case [θp+1=0 with p=1(p>1) for Grassmann (para-Grassmann) variables]. We show that the q-deformed commutation relations of the para-Grassmann variables lead naturally to consider q-deformed quadratic forms related to multiparametric deformations of GL (n) and their corresponding q-determinants. We suggest a possible application to the study of disordered systems.

GENERALIZED DEFORMED PARA-BOSE OSCILLATOR AND NONLINEAR ALGEBRAS

Generalized deformed commutation relations for a single mode para-Bose oscillator and for a system of two para-Bose oscillators are constructed. It turns out that generalized deformed para-Bose oscillators are not, in general, exactly independent. Furthermore, we also discuss about the Fock space corresponding to generalized deformed para-Bose oscillators. Finally, we show how SU(2) and SU(1, 1) generators can be constructed in terms of generalized deformed para-Bose creation and annihilation operators. The algebras SU(2) and SU(1, 1) of generalized deformed oscillators14,18 are the special cases of generalized deformed para-Bose oscillators algebras but, interestingly, they have the same form.