“…In [27], a full BRST formulation for the conic constrained motion has been achieved with its corresponding conserved BRST charge obtained in an operatorial quantization framework, while in [28] the symplectic Faddeev-Jackiw-BarcelosNeto-Wotzasek (FJBW) quantization approach has been employed with a thorough calculation of all Faddeev-Jackiw brackets leading to a gauge-invariant description for that model. The general solution and quantum algebra realization in terms of differential operators for the non-relativistic case has been obtained in detail in [29]. In spite of being constructed initially for comparative purposes, the models originally introduced in references [18,27,28] considerably grew up and acquired proper live interest being subsequently used as starting points for further discussions regarding (anti-)(co-)BRST symmetry [30,31], superfields [32], firstorder formalism and gauge invariance [33], Batalin-Fradkin-Fradkina-Tyutin (BFFT) Abelian conversion [34] and gauge-unfixing [35], giving rise to important genuine applications in field theory such as the Lorentz violating bumblebee model [34] and the non-linear sigma model [22,35].…”