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Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the $d$ dimensional Riemann space-time. Theory of canonical transformations, which relate equivalent…
The complete, missing, Hamiltonian treatment of the standard SU(3)xSU(2)xU(1) model with Grassmann-valued fermion fields in the Higgs phase is given. We bypass the complications of the Hamiltonian theory in the Higgs phase, resulting from…
The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may…
In Einstein's gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group ${A}(4,R)$ and of its subgroup…
The most prominent realization of gravity as a gauge theory similar to the gauge theories of the standard model comes from enlarging the gauge group from the Lorentz group to the de Sitter group. To regain ordinary Einstein-Cartan gravity…
The Dirac constraint formalism is applied to linearized gravity to determine the structure of constraints and construct the canonical Hamiltonian. The diffeomorphism invariance of the Lagrangian is retrieved by a nontrivial generalization…
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…
The status of canonical reduction for metric and tetrad gravity in space-times of the Christodoulou-Klainermann type, where the ADM energy rules the time evolution, is reviewed. Since in these space-times there is an asymptotic Minkowski…
Beside diffeomorphism invariance also manifest SO(3,1) local Lorentz invariance is implemented in a formulation of Einstein Gravity (with or without cosmological term) in terms of initially completely independent vielbein and spin…
A generalization of the Lagrangian introduced earlier in [2011 {\it J. Phys. G} ${\bf 37}$ 105001] for a classical color spinning particle interacting with background non-Abelian gauge and fermion fields for purpose of considering a change…
We study the transformation leading from Arnowitt, Deser, Misner (ADM) Hamiltonian formulation of General Relativity (GR) to the $\Gamma\Gamma$ metric Hamiltonian formulation derived from the Lagrangian density which was firstly proposed by…
In this paper, we discuss a gravitational theory based on the generalized gauge field. Our Lagrangian is invariant not only under local Lorentz transformation and the ordinary gauge transformation but also under a new gauge transformation.…
It is proven that the usual quadratic general-covariant Lagrangian for the Dirac field leads to a symmetric, divergence-free energy-momentum tensor in the standard Riemannian framework of space-time without torsion, provided the tetrad…
We propose a simple, nonlocal modification to general relativity (GR) on large scales, which provides a model of late-time cosmic acceleration in the absence of the cosmological constant and with the same number of free parameters as in…
We investigate the interplay between Horava-Lifshitz (HL) gravity and more general theories where the local Hamiltonian constraint is lost, for example due to the time variability of the Lagrangian (e.g. via its parameters) where time is…
The $(3 + 1)$-dimensional (generalized) Dirac equation is shown to have the same form as the equation expressing the condition that a given point lies on a given line in 3-dimensional projective space. The resulting Hamiltonian with a…
We suggest model equations, which, from some point of view, describe local interaction of three physical fields: a field of matter, an electromagnetic field and a gravitational field. A base of the model is a field of matter described by…
The idea of this contribution is to suggest a way to get rid of gravity as a dynamical space time approximately in cosmology and thus be able to use Hamiltonian formulation ignoring the gravitational degrees of freedom, treating them just…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
We analyze the constraints of general coordinate invariance for quantum theories possessing conformal symmetry in four dimensions. The character of these constraints simplifies enormously on the Einstein universe $R \times S^3$. The…