Front Matter

Casimir operators induced by the Maurer–Cartan equations

“…Although in these examples the Maurer-Cartan equations do not provide the rational invariant itself, they give the commuting polynomials that intervene in it 4 . This means that the invariant has the form…”

“…For these the invariants are specially useful, since they enable us to express the Hamiltonian of the system in terms of the Casimir operators of a Lie algebra and some of its Lie subalgebras (e.g., the interaction boson model) [1][2][3]. Other situations involving the invariants of an algebra and certain of its subalgebras appear in connection with symmetry breaking problems [4].…”

su (2) Lie algebra approach for the Feynman propagator of the one-dimensional harmonic oscillator

“…On the other hand, compact and non-compact Lie algebras have been successfully applied in studying several quantum systems [8]. For some solvable potentials, the existence of constants of motion and certain differential operators, which satisfy a Lie algebra, have been fundamental in obtaining the corresponding ground state, the ladder operators and the energy spectra.…”

Thesu(1, 1) dynamical algebra from the Schrödinger ladder operators forN-dimensional systems: hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator

“…A systematic method to find both compact and non-compact algebra generators for a given system has not still developed. These generators have been intuitively found and forced them to close an algebra, as it is extensively shown in [14,15]. For the most important central-potential problems, the hydrogen atom and the isotropic harmonic oscillator, algebraic treatments by means of compact and non-compact groups are known [16,17].…”