Related papers: Exactly Soluble Sector of Quantum Gravity
After reviewing how Albert Einstein's general relativity (GR) can be viewed as a gauge theory of the Poincar\'e algebra, we show how \'Elie Cartan's geometric formulation of Newtonian gravity (Newton-Cartan gravity) can be viewed as a gauge…
In the framework of the theory of scale relativity, we suggest a solution to the cosmological problem of the formation and evolution of gravitational structures on many scales. This approach is based on the giving up of the hypothesis of…
This research is an extension of the author's article \cite{zar}, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein's theory of…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
A nonpertubative approach to quantum gravity using precanonical field quantization originating from the covariant De Donder-Weyl Hamiltonian formulation which treats space and time variables on equal footing is presented. A generally…
We propose a nonlocal field theory for gravity in presence of matter consistent with perturbative unitarity, quantum finiteness, and other essential classical properties that we are going to list below. First, the theory exactly reproduces…
The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
We present a pedagogical discussion of the Coriolis field, emphasizing its not-so-well-understood aspects. We show that this field satisfies the field equations of the so-called Newton-Cartan theory, a generalization of Newtonian gravity…
We develop a semiclassical theory of modified gravity with nontrivial spacetime torsion. In particular, we show that the semiclassical treatment can be axiomatized in the case of Einstein--Cartan theory with a nonminimally coupled, free…
Quantum field theory successfully explains the origin of all fundamental forces except gravity due to the renormalizability problem. In this paper, we proposed a topological scenario to understand this puzzle. First, we proposed a $3+1$D…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
The cosmological implications of the Covariant Canonical Gauge Theory of Gravity (CCGG) are investigated. We deduce that, in a metric compatible geometry, the requirement of covariant conservation of matter invokes torsion of space-time. In…
We study Kaluza-Klein reduction in Newton-Cartan gravity. In particular we show that dimensional reduction and the nonrelativistic limit commute. The resulting theory contains Galilean electromagnetism and a nonrelativistic scalar. It…
Connections compatible with degenerate metric structures are known to possess peculiar features: on the one hand, the compatibility conditions involve restrictions on the torsion; on the other hand, torsionfree compatible connections are…
We give a detailed account of the cyclic $L_\infty$-algebra formulation of general relativity with cosmological constant in the Einstein-Cartan-Palatini formalism on spacetimes of arbitrary dimension and signature, which encompasses all…
We construct a "stringy" version of Newton-Cartan gravity in which the concept of a Galilean observer plays a central role. We present both the geodesic equations of motion for a fundamental string and the bulk equations of motion in terms…
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…
The problem of time and the quantization of three dimensional gravity in the strong coupling regime is studied following path integral methods. The time is identified with the volume of spacetime. We show that the effective action describes…