Quantum-group description of decaying particles

Bosonic algebras and their inhomogeneous invariance quantum groups

“…Since the elements of transformation matrix T have coproduct,counit and antipode one can state that the transformation is a quantum group and this quantum group is called as the Bosonic Inhomogeneous Symplectic Quantum Group, BISp(2d) [5], [6].…”

The multi-dimensional q-deformed bosonic Newton oscillator and its inhomogeneous quantum invariance group

“…Their hermitian conjugates are denoted by using * notation. Construction of the above transformation matrix will be meaningless unless the non zero elements of matrix M satisfy algebraic relations not only consistent among themselves but also belonging to a Hopf algebra [1][2][3][4][5][11][12][13][14][15][16]. Before writing what these algebraic relations are, let us write the transformed form of the generators of the two dimensional Newton oscillator algebra…”

“…To say that successive application of transformations, identity transformation, and inverse transformation are meaningful, the algebraic structure defined by the elements of the transformation matrix M should be a Hopf algebra [11]. The Hopf algebra structure of this system can be studied by defining coproduct, counit, and antipode…”

The Inhomogeneous Quantum Invariance Group of The Two Parameter Deformed Boson Algebra

“…as a transformation matrix [15][16][17][18][19][20][21] such that it acts on 4 × 1 column vector V by matrix co-multiplication. The elements of the column vector V are the generators of the algebra defined by (9) and (10), namely,…”