GEOMETRIC PHASES IN THE QUANTISATION OF BOSONS AND FERMIONS
After reviewing geometric quantisation of linear bosonic and fermionic systems, we study the holonomy of the projectively flat connection on the bundle of Hilbert spaces over the space of compatible complex structures and relate it to the Maslov index and its various generalisations. We also consider bosonic and fermionic harmonic oscillators parametrised by compatible complex structures and compare Berry’s phase with the above holonomy.
Abstract Kim et al. (Appl. Math. Inf. Sci. 9(6):1-6, 2015) consider the q -extensions of Boole polynomials. In this paper, we consider Witt-type formula for the q -Boole polynomials with weights and derive some new interesting identities and properties of those polynomials and numbers from the Witt-type formula which are related to special polynomials and numbers.