A Gauge Invariant Description for the General Conic Constrained Particle from the FJBW Iteration Algorithm

General Solution and Canonical Quantization of the Conic Path Constrained Second-Class System

“…It is possible to obtain enlightening insights about quantum field theory by exploring specific features of crafty properly designed quantum mechanical models. As a short sample, we mention the references [1,2,3,4,5,6,7,8,9]. In [1] we see an alternative mechanical model for spinning particles, while in [2] a quantum mechanical gauge model is constructed from a particle on a circle mimicking the massive Schwinger model in order to discuss the Strong CP Problem.…”

“…A supervariable approach to a supersymmetric quantum mechanical model can be seen in [4]. A free particle moving along a conic curve has been discussed in references [5,6] whilst a more general Hamiltonian mechanical model with gauge invariance, treated via the Dirac-Bergmann constraints algorithm, can be seen in [7]. Connections between field theory and classical mechanics through the gauge principle as a local symmetry have been investigated in [8].…”

“…The problem is characterized as a singular Dirac-Bergmann second-class system governed by coupled non-linear differential equations whose general solution is obtained here in full detail. Some aspects of a simplified version of this model have been considered in [5,6], which actually generalize a few ideas already seen in [13]. Aiming at a direct analogy with quantum chromodynamics, reference [13] elaborates on different possible descriptions for the motion of a particle along a circular path as a constrained system.…”

“…The Faddeev-Popov ghosts of QCD are shown to have a similar counterpart in the mechanical model which also enjoys a natural BRST symmetry. The main raw ideas present in [13], some of them introduced in an ad hoc manner, were further justified, explained, generalized and organized in a systematic way in references [5,6]. Starting from two consistent Lagrangian and Hamiltonian mechanical models, the BRST quantization of a conic constrained particle is fully implemented in [5] whereas a symplectic approach via FJBW 4 can be seen in [6].…”

“…The main raw ideas present in [13], some of them introduced in an ad hoc manner, were further justified, explained, generalized and organized in a systematic way in references [5,6]. Starting from two consistent Lagrangian and Hamiltonian mechanical models, the BRST quantization of a conic constrained particle is fully implemented in [5] whereas a symplectic approach via FJBW 4 can be seen in [6]. Despite being constructed initially for comparative purposes, the model introduced in references [5,6,13] grew up and acquired interest in itself being subsequently used as a starting point for further discussions regarding (anti-)BRST symmetry [16], superfield formalism [17] and BFFT 5 Abelian conversion [21], giving rise to interesting applications in field theory such as the Lorentz breaking bumblebee model [21] and the non-linear sigma model [22].…”