We carry out the canonical analysis of a covariant version unimodular gravity in terms connection representation. then proceed to quantize this theory by implementing Dirac procedure. confirm whether and how Kodama state, which is solution quantum general relativity, can be extended into gravity. Finally, we discuss difference states between gravity, original relativity.

The general relativity theory is redefined equivalently in almost Kähler variables: symplectic form, θ[g], and canonical symplectic connection, D̂[g] (distorted from the Levi–Civita connection by a tensor constructed only from metric coefficients and their derivatives). The fundamental geometric and physical objects are uniquely determined in metric compatible form by a (pseudo) Riemannian metri...

We propose an unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo–Riemannian manifolds enabled with 1) a nonholonomic 2+2 distribution defining a nonlinear connection (N–connection) structure and 2) an Arnowitt–Deser–Misner 3+1 decomposition. The Ashtekar– B...

Based on the previously formulated mathematical model of a statistical system with scalar interaction fermions, cosmological based one-component doubly charged degenerate fermions interacting an asymmetric doublet-canonical and phantom fields-is studied. The connection presented studied models two-component fermion systems is investigated. asymptotic limiting properties are investigated, it sho...

Abstract A geometric decomposition previously adopted in areas of nonlinear continuum mechanics and soliton theory is applied to a two-dimensional time-independent magnetohydrodynamic system obtain reduction canonical third order equation subject constraint. Novel classes exact solutions the are thereby constructed. Connection made with kinematic conditions which attend certain steady motions f...

We study Hermitian metrics with a Gauduchon connection being "K\"ahler-like", namely, satisfying the same symmetries for curvature as Levi-Civita and Chern connections. In particular, we investigate $6$-dimensional solvmanifolds invariant complex structures trivial canonical bundle metrics. The results this case give evidence two conjectures that are expected to hold in more generality: first, ...

A canonical form for elements of a lattice freely generated by a partial lattice is given. This form agrees with Whitman’s canonical form for free lattices when the partial lattice is an antichain. The connection between this canonical form and the arithmetic of the lattice is given. For example, it is shown that every element of a finitely presented lattice has only finitely many minimal join ...

We consider the classical Hamiltonian of interior Schwarzschild black hole in Ashtekar-Barbero connection formalism. Then, inspired by generalized uncertainty principle models, we deform canonical algebra and derive effective dynamics model under this modification. show that such a deformation leads to resolution singularity minimum nonzero radius for infalling 2-spheres, provided parameters ar...

the main objective of this study was using of canonical correlation analysis (cca) to find relations between 15 different variables of seed emergence and seedling growth related characteristics of seven important crop that were classified in three groups. the studied groups of variables were included physical characteristics (seed weight, seed length, seed density, water absorption and water co...