Related papers: q-Conformal Invariant Equations and q-Plane Wave S…
In this paper, we consider a family of $n$-dimensional, higher-curvature theories of gravity whose action is given by a series of dimensionally extended conformal invariants. The latter correspond to higher-order generalizations of the…
A short survey of some material related to conformal general relativity (CGR), integrable Weyl geometry, and Dirac-Weyl (DW) theory is given which suggests that CGR is essentially equivalent to DW with quantum mass equivalent to conformal…
We investigate the evolution of cosmological perturbations generated during de Sitter inflation in the conformal gravity. Primordial gravitational waves are composed of vector and tensor modes. We obtain the constant vector and tensor power…
Fully covariant wave equations predict the existence of a class of inertial-gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical fields, but, by conforming to general…
A conformal gauge theory is used to describe and unify myriad electromechanical and magnetomechanical coupling effects observed in solid continua. Using a space-time pseudo-Riemannian metric in a finite-deformation setup and exploiting the…
We discuss conformally flat plane wave solutions of Einstein equations depending on the plane wave phase $\xi=\omega\tau-{\bf qx}$, where $\tau$ is the conformal time. We show that ideal fluid Einstein equations and scalar fields with…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
We analyse the dynamical properties of disformally transformed theories of gravity. We show that disformal transformation typically introduces novel degrees of freedom, equivalent to the mimetic dark matter, which possesses a Weyl-invariant…
When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
In this note we outline the history of q-deformations; indicate their physical shortcomings; suggest their apparent resolution via an invariant formulation based on a new mathematics of genotopic type; and point out their expected physical…
We construct a family of irreducible representations of the quantum plane and of the quantum Weyl algebra over an arbitrary field, assuming the deformation parameter is not a root of unity. We determine when two representations in this…
Static, spherically symmetric solutions to the semi-classical Einstein equation are studied, including the effect of the quantum energy-momentum tensor for conformal matters with 4D Weyl anomaly. Through both perturbative and…
We shall present here the causal interpretation of canonical quantum gravity in terms of new variables. Then we shall apply it to the minisuperspace of cosmology. A vacuum solution of quantum cosmology is obtained and the Bohmian trajectory…
In this letter we introduce a particular solution for parallel electric and magnetic fields, in a gravitational background, which satisfy free-wave equations and the phenomenology suggested by astrophysical plasma physics. These free-wave…
In this review we consider the quadratic Metric-Affine Gauge gravity Lagrangian, which contains all the algebraic invariants up to quadratic order in torsion, nonmetricity and curvature. The goal will be to collect the known exact solutions…
The extended-BMS algebra of asymptotically flat spacetime contains an SO(3,1) subgroup that acts by conformal transformations on the celestial sphere. It is of interest to study the representations of this subgroup associated with…
The metaplectic covariance for all forms of the Weyl-Wigner-Groenewold-Moyal quantization is established with different realizations of the inhomogeneous symplectic algebra. Beyond that, in its most general form $W_{\infty}$ -covariance of…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…