Inhomogeneous quantum invariance group of commuting fermions

Abstract

Since the middle of the twentieth century, physicists have concentrated on finding quantum counterparts of classical systems. When a classical system is quantized its invariance group may still be a classical group. In the nineteen-eighties it was shown that when some classical systems are quantized, their classical group becomes a quantum group so that the system is invariant under a quantum group. So quantum groups play an important role in carrying physical properties to the quantum world. In this thesis we will first review the fermionic and the bosonic algebras and their inhomogeneous invariance quantum groups. Then we will introduce the commuting fermion algebra and construct its inhomogeneous invariance quantum group.