Related papers: Symplectic embedding and Hamilton-Jacobi analysis …
We convert the second class Proca model into a first class theory by using the generalised prescription of Batalin, Fradkin and Tyutin. We then show how a basic set of gauge invariant fields in the embedded model can be identified with the…
Dirac formalism of Hamiltonian constraint systems is studied for the noncommutative Abelian Proca field. It is shown that the system of constraints are of second class in agreement with the fact that the Proca field is not guage invariant.…
The BRST quantization of the Abelian Proca model is performed using the Batalin-Fradkin-Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class…
We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical…
The Hamilton-Jacobi formalism for a geodetic brane-like universe described by the Regge-Teitelboim model is developed. We focus on the description of the complete set of Hamiltonians that ensure the integrability of the model in addition to…
This work contains a brief and elementary exposition of the foundations of Poisson and symplectic geometries, with an emphasis on applications for Hamiltonian systems with second-class constraints. In particular, we clarify the geometric…
A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of…
We apply the Batalin-Tyutin Hamiltonian method to the Abelian Proca model in order to convert a second class constraint system into a first class one systematically by introducing the new fields. Then, according to the BFV formalism we…
In this paper we reformulate Abelian and non-Abelian noninvariant systems as gauge invariant theories using a new constraint conversion scheme, developed on the symplectic framework. This conversion method is not plagued by the ambiguity…
We review the Batalin-Tyutin approach of quantising second class systems which consists in enlarging the phase space to convert such systems into first class. The quantisation of first class systems, it may be mentioned, is already well…
A new procedure for the construction of higher-dimensional Lie-Hamilton systems is proposed. This method is based on techniques belonging to the representation theory of Lie algebras and their realization by vector fields. The notion of…
Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key…
In the symplectic Lagrangian framework we newly embed an irreducible massive vector-tensor theory into a gauge invariant system, which has become reducible, by extending the configuration space to include an additional pair of scalar and…
This paper is devoted to study gauge embedding of either commutative and noncommutative theories in the framework of the symplectic formalism. We illustrate our ideas in the Proca model, the irrotational fluid model and the noncommutative…
The second class constraints algebra of the abelian Chern-Simons theory is rigorously studied in terms of the Hamiltonian embedding in order to obtain the first class constraint system. The symplectic structure of fields due to the second…
We show how to systematically derive the exact form of local symmetries for the abelian Proca and CS models, which are converted into first class constrained systems by the BFT formalism, in the Lagrangian formalism. As results, without…
Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson…
We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not…
The Symplectic Pontryagin method was introduced in a previous paper. This work shows that this method is applicable under less restrictive assumptions. Existence of solutions to the Symplectic Pontryagin scheme are shown to exist without…
The symplectic analysis, initiated by Faddeev and Jackiw, is applied to the first order (Palatini) form of the Einstein-Hilbert action in 1 + 1 dimensions. The constraints that arise are shown to result in the same gauge transformations…