Generalized Hooke groups and the mass-spectrum problem

Abstract

We briefly recall the notion of internal structure and the relativistic covariant method [introduced in Beau and Horchani, J. Math. Phys. 20, 1700 (1979)] of unifying external and internal structures leading to a kinematical Lie algebra. In this framework we propose a concept of dynamical development of the physical systems defined by this Lie algebra. So we obtain some Lie algebras, a generator of which (the Hamiltonian) gives rise to various mass formulas capable of describing the hadron spectrum; we make use of both unitary irreducible global representations and partially integrable, Schur-irreducible, symmetric local representations.