Related papers: Covariant hamiltonian for gravity coupled to $p$-f…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
In this short note we perform canonical analysis of the theory invariant under restricted diffeomorphism so that the action contains kinetic term for determinant of metric. We find corresponding Hamiltonian and determine structure of…
We consider the Palatini formalism of gravity with cosmological constant $\Lambda$ coupled to a scalar field $\phi$ in $n$-dimensions. The $n$-dimensional Einstein equations with $\Lambda$ can be derived by the variation of the coupled…
Einstein's general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric…
The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism…
I review the formalism of loop quantum gravity, in both its real and complex formulations, and spin foam theory which is its path integral counterpart. Spin networks for non-compact groups are introduced (following hep-th/0205268) to deal…
We develop the formalism for canonical reduction of $(1+1)$--dimensional gravity coupled with a set of point particles by eliminating constraints and imposing coordinate conditions. The formalism itself is quite analogous to the…
We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation $\mathbf{F}=\frac{d\mathbf{p}}{dt}$, where $\mathbf{F}$ is the 3D force and $\mathbf{p}=m_0\gamma\mathbf{v}$ is…
We construct covariant theories incorporating fluctuating boundaries and soft cutoffs by introducing dynamical reference frames (DRFs). This framework generalizes the covariant action from a hard-cutoff to a soft-cutoff formulation,…
In this paper we perform in a manifestly $SO(n-1,1)$ [or, alternatively $SO(n)$] covariant fashion, the canonical analysis of general relativity in $n$ dimensions written as a constrained $BF$ theory. Since the Lagrangian action of the…
We apply the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as…
The covariant canonical formalism for four-dimensional BF theory is performed. The aim of the paper is to understand in the context of the covariant canonical formalism both the reducibility that some first class constraints have in Dirac's…
First-order general relativity in $n$ dimensions ($n \geq 3$) has an internal gauge symmetry that is the higher-dimensional generalization of three-dimensional local translations. We report the extension of this symmetry for $n$-dimensional…
We introduce a phase space with spinorial momenta, corresponding to fermionic derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is a generalisation of the covariant De Donder-Weyl Hamiltonian formulation on this…
In the gauge theory of gravity based on the Poincare group (the semidirect product of the Lorentz group and the spacetime translations) the mass (energy-momentum) and the spin are treated on an equal footing as the sources of the…
New approach to quantization of the relativistic Majorana field is presented. It is based on expansion of the field into eigenfunctions of the axial momentum -- a novel observable introduced recently. Relativistic invariance is used as the…
I illustrate a simple hamiltonian formulation of general relativity, derived from the work of Esposito, Gionti and Stornaiolo, which is manifestly 4d generally covariant and is defined over a finite dimensional space. The spacetime…
A systematic Hamiltonian formulation of the Einstein-Cartan system, based on the Hilbert-Palatini action with the Barbero-Immirzi and cosmological constants, is performed using the traditional ADM decomposition and without fixing the time…
The non-relativistic Goedecke equation (1975), which describes the motion of a point charge taking into account the radiation reaction, has no "runaway" solutions. A "physical" method of covariant generalization of this equation is…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…