Related papers: Symplectic algorithm for systems with second-class…
We extend the quantization \`a la Faddeev-Jackiw for non-autonomous singular systems. This leads to a generalization of the Schr\"odinger equation for those systems. The method is exemplified by the quantization of the damped harmonic…
The symplectic analysis of a four dimensional $BF$ theory in the context of the Faddeev-Jackiw symplectic approach is performed. It is shown that this method is more economical than Dirac's formalism. In particular, the complete set of…
The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we…
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…
In this work, a conformable singular system with second-class constraints is discussed. The conformable Poisson bracket (CDB) of two functions is defined. and, the Dirac theory is developed to be applicable to conformable singular systems.…
We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing…
We show that the iterative Faddeev-Jackiw (FJ) reduction for singular Lagrangian systems constitutes a geometrically constrained instance of the Matrix Bordering Technique (MBT). For a first-order Lagrangian with singular pre-symplectic…
The conformal affine sl(2) Toda model coupled to matter field is treated as a constrained system in the context of Faddeev-Jackiw and the (constrained) symplectic schemes. We recover from this theory either, the sine-Gordon or the massive…
The Jackiw-Teitelboim model written as a BF theory in two dimensions is analyzed by using the Dirac's and Faddeev-Jackiw formalism. The analysis consists in finding the full structure of the constraints, the gauge transformations, the…
We review and compare different variational formulations for the Schr\"{o}dinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm…
D-dimensional constrained systems are studied with stochastic Lagrangian and\break Hamiltonian. It is shown that stochastic consistency conditions are second class constraints and Lagrange multiplier fields can be determined in…
The Faddeev-Jackiw Hamiltonian Reduction approach to constrained dynamics is applied to the collective coordinates analysis of non-linear waves, and compared with the alternative procedure known as symplectic formalism.
The classification of the regularization ambiguity of 2D fermionic determinant in three different classes according to the number of second-class constraints, including the new faddeevian regularization, is examined and extended. We found a…
We consider the master Lagrangian of Deser and Jackiw, interpolating between the self-dual and the Maxwell-Chern-Simons Lagrangian, and quantize it following the symplectic approach, as well as the traditional Dirac scheme. We demonstrate…
We quantize the chiral Schwinger Model by using the Batalin-Tyutin formalism. We show that one can systematically construct the first class constraints and the desired involutive Hamiltonian, which naturally generates all secondary…
Dirac algorithm allows to construct Hamiltonian systems for singular systems, and so contributing to its successful quantization. A drawback of this method is that the resulting quantized theory does not have manifest Lorentz invariance.…
The general conditions for the applicability of the Faddeev-Jackiw approach to gauge theories are studied. When the constraints are effective a new proof in the Lagrangian framework of the equivalence between this method and the Dirac…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
The aim of this work is to discuss some aspects of the reduction of order formalism in the context of the Fadeev-Jackiw symplectic formalism, both at the classical and the quantum level. We start by reviewing the symplectic analysis in a…
The Jackiw-Rajaraman version of the chiral Schwinger model is studied as a function of the renormalization parameter. The constraints are obtained and they are used to carry out canonical quantization of the model by means of Dirac…