Representations ofSU(1,1) in non-commutative space generated by the Heisenberg algebra

0 Representations of SU ( 1 , 1 ) in Non - commutative Space Generated by the Heisenberg Algebra

SU(1, 1) is considered as the automorphism group of the Heisenberg algebra H . The basis in the Hilbert space K of functions on H on which the irreducible representations of the group are realized is explicitly constructed. The addition theorems are derived. March 2000

Representations of the Heisenberg algebra by difference operators

We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our construction for two types of shifts: (1) real shifts, (2) purely imaginary shifts. The representations involving imaginary shifts are free of spectrum doublin...

Non-commutative combinatorial algebra

Embedding of a 2D Graphene System in Non-Commutative Space

The BFT approach is used to formulate the electronic states in graphene through a non-commutative space in the presence of a constant magnetic field B for the first time. In this regard, we introduce a second class of constrained system, which is not gauge symmetric but by applying BFT method and extending phase space, the second class constraints  converts  to the first class constraints so th...

Commutative Algebra Commutative Algebra : General