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Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
The {\it {gauge - fixing} } and {\it gaugeless } methods for reducing the phase space in the generalized Hamiltonian dynamics are compared with the aim to define the class of admissible gauges . In the gaugeless approach, the reduced phase…
We study a gravitational action which is a linear combination of the Hilbert-Palatini term and a term quadratic in torsion and possessing local Poincare invariance. Although this action yields the same equations of motion as General…
There is a gap that has been left open since the formulation of general relativity in terms of Ashtekar's new variables namely the treatment of asymptotically flat field configurations that are general enough to be able to define the…
There is a gap that has been left open since the formulation of general relativity in terms of Ashtekar's new variables namely the treatment of asymptotically flat field configurations that are general enough to be able to define the…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…
The coadjoint orbit method is applied to the construction of Hamiltonian dynamics of massless particles of arbitrary helicity. The unusual transformation properties of canonical variables are interpreted in terms of nonlinear realizations…
We study the action for the three-space formalism of General Relativity, better known as the BF\'O (Barbour--Foster--\'O Murchadha) action, which is a square-root BSW (Baierlein--Sharp--Wheeler) action. In particular, we explore the…
We develop a general canonical quantization scheme for $k$-essence cosmology in scalar-tensor theory. Utilizing the Dirac-Bergmann algorithm, we construct the Hamiltonian associated with the cosmological field equations and identify the…
Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity.…
One of the virtues of the Ashtekar variables is the simplification of the initial value constraints for gravity. In the case of self-dual variables this entails a complexification of the phase space which comes at the expense of having to…
The Palatini action is based on vector-valued one forms or frames and SL(2,C) connections on R^4. Using the spacetime split of R^4 as a direct sum of R^3 and R^1, the Gauss law in this paper is treated on a Hilbert space. This is achieved…
We use the freedom available in hybrid loop quantum cosmology to split the degrees of freedom between the geometry and the matter fields so as to build a quantum field theory for the matter content with good quantum properties. We…
We formulate axisymmetric general relativity in terms of real Ashtekar--Barbero variables. We study the constraints and equations of motion and show how the Kerr, Schwarzschild and Minkowski solutions arise. We also discuss boundary…
We construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered from an entirely new perspective.…
By using the Hamilton-Jacobi [HJ] framework the three dimensional Palatini theory plus a Chern-Simons term [PCS] is analyzed. We report the complete set of $HJ$ Hamiltonians and a generalized $HJ$ differential from which all symmetries of…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are…
In this paper, we are going to discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional General Relativity and Supergravity developed in our…