From Majorana Neutrino and Dark Neutrino 0 to Dark Spin Particles

In current theory of particle physics, the values of Casimir Operator, that is abbreviated to CO, of spin angular momentum for elementary particles are thought to be greater than zero.

Algebraic structure of Dirac–Pauli equation with account to AMM of neutron in the presence of magnetic field with cylindrical symmetry

The eigenvalues and eigenfunctions of Dirac–Pauli equation have been obtained for a neutron with anomalous magnetic moment (AMM) in the presence of a strong magnetic field with cylindrical symmetry. In our calculations, the Nikiforov and Uvarov (NU) method has been used. Using the eigenfunctions and construction of the ladder operators, we show that these generators satisfy su(2) Lie algebra and computed the second-order Casimir operator of the lie algebra.

Split Casimir Operator and Universal Formulation of the Simple Lie Algebras

We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in adjoint representation. By means of these characteristic identities, for all simple Lie algebras we derive explicit formulae for invariant projectors onto irreducible subrepresentations in T⊗2 in the case when T is the adjoint representation. These projectors and characteristic identities are considered from the viewpoint of the universal description of the simple Lie algebras in terms of the Vogel parameters.

Generalized deformed SU(2) algebras in Nuclear Physics

A generalized deformed algebra SUφ(2), characterized by a structure function Φ. is obtained. The usual SU(2) and SUq(2) algebras correspond to specific choices of the structure function Φ. The action of the generators of the algebra on the relevant basis vectors, as well as the eigenvalues of the Casimir operator, are easily obtained. Possible applications in improving phenomenological nuclear models are discussed.

Generalized Casimir operators

Let [Formula: see text] be symmetrizable Kac–Moody Lie algebra. In this paper, we describe a new class of central operators generalizing the Casimir operator. We also prove some properties of these operators and show that these operators move highest weight vectors to new highest weight vectors.