Zlosnik, "Exploring Cartan gravity with

dynamical symmetry breaking," Classical and Quantum Gravity, vol.

We furthermore prove that the models with pure Calogero potentials and those with the extra DFF term possess isomorphic

dynamical symmetry (super) algebras.

Table 1: Equilibrium values of the parameters A2, A3, A4 in the large N limit for transition from

dynamical symmetry limit U(5) to

dynamical symmetry limit SU(3) as an illustrative example.

Remaining chapters formally describe

dynamical symmetry in Hamiltonian mechanics, symmetries in classical Keplerian motion,

dynamical symmetry in Schrodinger quantum mechanics, spectrum-generating Lie algebras and groups admitted by Schrodinger equations,

dynamical symmetry of regularized hydrogen-like atoms, approximate dynamical symmetries in atomic and molecular physics, rovibronic systems, and

dynamical symmetry of Maxwell's equations.

Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics; non-relativistic and relativistic.

Later on, references [7, 8, 13] indicated a way of constructing the so-called "

dynamical symmetry algebra" by applying the FM to differential or difference equations [3, 11, 12] and then this technique has been used to consider some particular instances of q-hypergeometric difference equations.

"[We] have shown that the

dynamical symmetry associated with motion in [the relevant kind of force field] provides extremely stringent limits on any possible deviation of the number of dimensions from the integer value of 3, on both atomic and astronomical length scales," they conclude.

For Mq = 0 the Lagrangian retains the full SU(4) symmetry but, in an analogy with QCD, one might expect the

dynamical symmetry breaking by vacuum expectation value <[bar.U]U + [bar.D]D> [not equal to] 0.

FAKHRI, The embedding of parasupersymmetry and

dynamical symmetry into GL(2, c) group, Ann.

The

dynamical symmetry E(5) describe the phase transition between a spherical vibrator (U(5)) and [gamma]-soft rotor (O(6)) and the X(5) for the critical point of the spherical to axially deformed (SU(3)) transition.

We review the concept of

dynamical symmetry in section 5.

It is well know that the

dynamical symmetry associated with U(5) corresponds to a spherical shape [beta] = 0, the

dynamical symmetry SU(3) is associated with an axially deformed shape [beta] [not equal to] 0 and [gamma] = 0, [pi]/3 and the

dynamical symmetry O(6) is related to a y-unstable deformed shape [beta] [not equal to] 0 and [gamma]-independent.