Related papers: Conic Constrained Particle Quantization within the…
The Legendre transformation on singular Lagrangians, e.g. Lagrangians representing gauge theories, fails due to the presence of constraints. The Faddeev-Jackiw technique, which offers an alternative to that of Dirac, is a symplectic…
There is a review of the physical theories needing Dirac-Bergmann theory of constraints at the Hamiltonian level due to the existence of gauge symmetries. It contains: i) the treatment of systems of point particles in special relativity…
The BRST-anti-BRST covariant extension is suggested for the split involution quantization scheme for the second class constrained theories. The constraint algebra generating equations involve on equal footing a pair of BRST charges for…
We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the…
The general procedure of constructing a consistent covariant Dirac-type bracket for models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial…
A toy model (suggested by Klauder) is analyzed from the perspective of First Class and Second Class Dirac constrained systems. The comparison is made by turning a First Class into a Second Class system with the introduction of suitable…
Finite dimensional models that mimic the constraint structure of Einstein's General Relativity are quantized in the framework of BRST and Dirac's canonical formalisms. The first system to be studied is one featuring a constraint quadratic…
Classical mechanical systems with internal constraints will be examined using the extended symplectic formalism of Faddeev-Jackiw. We will derive the generalized brackets of the theory and the corresponding equations of motion. The…
By applying the Faddeev-Jackiw symplectic approach we systematically show that both the local gauge symmetry and the constraint structure of topologically massive gravity with a cosmological constant $\Lambda$, elegantly encoded in the…
In this paper we show how the BRST quantization can be applied to systems possessing only second-class constraints through their conversion to some first-class ones starting with our method exposed in [Nucl.Phys. B456 (1995)473]. Thus, it…
We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first…
This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to a classical model of a spinless relativistic particle as well as…
The nonholonomic constrained system with second-class constraints is investigated using the Hamilton-Jacobi (HJ) quantization scheme to yield the complete equations of motion of the system. Although the integrability conditions in the HJ…
A minor change in the Barcelos-Wotzasek (BW) symplectic algorithm for constrained systems is proposed. The change addresses some criticism that formalism has received, placing it on the same footing as Dirac's algorithm.
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…
We apply a new and mathematically rigorous method for the quantization of constrained systems to two-dimensional gauge theories. In this method, which quantizes Marsden-Weinstein symplectic reduction, the inner product on the physical state…
The loop quantization of Brans-Dicke theory (with coupling parameter $\omega\neq-3/2$) is studied. In the geometry-dynamical formalism, the canonical structure and constraint algebra of this theory are similar to those of general relativity…
We perform the canonical and path integral quantizations of a lower-order derivatives model describing Podolsky's generalized electrodynamics. The physical content of the model shows an auxiliary massive vector field coupled to the usual…
We study the presence of symmetry transformations in the Faddeev-Jackiw approach for constrained systems. Our analysis is based in the case of a particle submitted to a particular potential which depends on an arbitrary function. The method…
A generalized version is proposed for the field-antifield formalism. The antibracket operation is defined in arbitrary field-antifield coordinates. The antisymplectic definitions are given for first- and second-class constraints. In the…