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The Dirac constraint formalism is used to analyze the first order form of the Einstein-Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that…
A generalization of the Dirac's canonical quantization theory for a system with second-class constraints is proposed as the fundamental commutation relations that are constituted by all commutators between positions, momenta and Hamiltonian…
The purpose of this paper is to study in detail the constraint structure of the Hamiltonian and symplectic-Lagrangian descriptions for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the…
We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial…
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
We present a novel framework for quantizing constrained quantum systems in which the processes of quantization and constraint enforcement are performed simultaneously. The approach is based on an extension of the stationary action…
We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…
Following from a question of Wheeler, why does the Hamiltonian constraint ${\cal H}$ of GR have the particular form it does? A first answer, by Hojman, Kucha\v{r} and Teitelboim, is that using embeddability into spacetime as a principle…
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.
A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
It is shown that in the case of the spherically symmetric static backgrounds there is a gauge in which the Dirac equation is manifestly covariant under rotations. This allows us to separate the spherical variables like in the flat…
The most general dilaton gravity theory in 2 spacetime dimensions is considered. A Hamiltonian analysis is performed and the reduced phase space, which is two dimensional, is explicitly constructed in a suitable parametrization of the…
A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in…
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid…