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Dynamical invariants are derived for time-dependent systems with nonlinear equations of motion including nonharmonic damped systems. The concept of a dynamical algebra is discussed and its utility for the construction of dynamical invariants for nonharmonic systems is demonstrated. Finally we show the existence of dynamical invariants for some nonlinear quantum systems.

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Within the framework of the constituent quark model and a generalized Pauli principle, the diquark interaction energies in quark–gluon plasma are explicitly calculated. In particular, two-diquark interaction energies are computed using ϕ4-terms in the effective Lagrangian in the spirit of the Donoghue and Sateesh model (1988 Phys. Rev. D 38 360). We also account for the extended character of the diquark. These results are used to determine the coupling strengths for a variety of colour–spin two-diquark states. Equations of state for the diquark matter for a variety of cases are derived and subsequently the Tolman–Oppenheimer–Volkoff equations for the masses and radii of diquark stars are solved. In this work, we restrict ourselves to the study of only the non-strange version of diquarks.

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