Born's Reciprocal General Relativity Theory and Complex Non-Abelian Gravity as Gauge Theory of the Quaplectic Group: A Novel Path to Quantum Gravity (original) (raw)

Born’s Reciprocal Gravity in Curved Phase-Spaces and the Cosmological Constant

The main features of how to build a Born's Reciprocal Gravitational theory in curved phase-spaces are developed. The scalar curvature of the 8D cotangent bundle (phase space) is explicitly evaluated and a generalized gravitational action in 8D is constructed that yields the observed value of the cosmological constant and the Brans-Dicke-Jordan Gravity action in 4D as two special cases. It is found that the geometry of the momentum space can be linked to the observed value of the cosmological constant when the curvature in momentum space is very large, namely the small size of P is of the order of (1/R Hubble ). More general 8D actions can be developed that involve sums of 5 distinct types of torsion squared terms and 3 distinct curvature scalars R, P, S. Finally we develop a Born's reciprocal complex gravitational theory as a local gauge theory in 8D of the def ormed Quaplectic group that is given by the semi-direct product of U (1, 3) with the def ormed (noncommutative) Weyl-Heisenberg group involving four noncommutative coordinates and momenta. The metric is complex with symmetric real components and antisymmetric imaginary ones. An action in 8D involving 2 curvature scalars and torsion squared terms is presented.

Gauge theory of quantum gravity

2014

The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great challenge in physics. Here we present an alternative construction of quantum gravity in which the quantum gravitational degrees of freedom are described by the non-Abelian gauge fields characterizing topological non-triviality of the space-time. The quantum dynamics of the space-time thus corresponds to the superposition of the distinct topological states. Its unitary time evolution is described by the path integral approach. This result will also be suggested to solve some major problems in physics of the black holes.

Quantum Gravity from Noncommutative Spacetime

J.Korean Phys.Soc. 65 (2014) 1754-1798

We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of symplectic geometry rather than Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory and so gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, it is feasible to formulate a background independent quatum gravity where the prior existence of any spacetime structure is not a priori assumed but defined by fundamental ingredients in quantum gravity theory. This scheme for quantum gravity resolves many notorious problems in theoretical physics, for example, to resolve the cosmological constant problem, to understand the nature of dark energy and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture for what matter is. A matter field such as leptons and quarks simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative ⋆-algebra) of quantum gravity.

Algebraic Approach to Quantum Gravity III: Non-Commutative Riemannian Geometry

Quantum Gravity Mathematical Models and Experimental Bounds, 2007

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that arises naturally as the classical limit; a theory with nonsymmetric metric and a skew version of metric compatibilty. Meanwhile, in quantum gravity a key ingredient of our approach is the proposal that the differential structure of spacetime is something that itself must be summed over or 'quantised' as a physical degree of freedom. We illustrate such a scheme for quantum gravity on small finite sets.

Algebraic Approach to Quantum Gravity III: Non-Commmutative Riemannian Geometry

Quantum Gravity, 2000

Remarkable aspects and and unsolved problems in quantum gravity theory

Academia Letters, 2022

The search of a theory of quantum gravity (QG) which is consistent both with the principles of quantum mechanics as well as with the postulates of the classical Einstein theory of General Relativity (GR) has represented until recently one of the most challenging, long-standing debated and hard-to-solve conceptual problems of mathematical and theoretical physics alike. In fact, a basic crucial issue is about the possibility of achieving in the context of either classical or quantum relativistic theories, and in particular for a quantum theory of gravity, a truly coordinate-(i.e., frame-) independent representation, realized by 4-tensor notation of physical laws. This means that the latter theory must satisfy both the principles of general covariance and of manifest covariance with respect to the group of local point transformations (LPT-group), i.e., coordinate diffeomorphisms mutually mapping in each other different GR frames. These principles lie at the foundation of all relativistic theories and of the related physical laws. In fact, although the choice of special coordinate systems is always legitimate for all physical systems either discrete or continuous, including in particular classical and quantum gravity, the intrinsic objective nature of physical laws makes them frame-independent. For the same reason, since LPTs preserve the differential-manifold structure of space-time, these principles represent also a cornerstone of the standard formulation of GR, namely the Einstein field equations and the corresponding classical treatment of the gravitational field. The same principles should apply as well to the very foundations of quantum field theory

From general relativity to quantum gravity

Lecture Notes in Physics, 1982

In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature of GR is at the forefront. However, the short distance dynamics in the quantum theory are quite different from those of GR and classical spacetimes and gravitons emerge only in a suitable limit. Our emphasis is on communicating the key strategies, the main results and open issues. In the spirit of this volume, we focus on a few avenues that have led to the most significant advances over the past 2-3 decades. 1

Quantum gravity without Lorentz invariance

Journal of High Energy Physics, 2009

There has been a significant surge of interest in Hořava's model for 3+1 dimensional quantum gravity, this model being based on anisotropic scaling at a z = 3 Lifshitz point. Hořava's model, and its variants, show dramatically improved ultraviolet behaviour at the cost of exhibiting violation of Lorentz invariance at ultra-high momenta. Following up on our earlier note, Phys. Rev. Lett. 102 (2009) 251601 [arXiv:0904.4464 [hepth]], we discuss in more detail our variant of Hořava's model. In contrast to Hořava's original model, we abandon "detailed balance" and restore parity invariance. We retain, however, Hořava's "projectability condition" and explore its implications. Under these conditions, we explicitly exhibit the most general model, and extract the full classical equations of motion in ADM form. We analyze both spin-2 and spin-0 graviton propagators around flat Minkowski space. We furthermore analyze the classical evolution of FLRW cosmologies in this model, demonstrating that the higher-derivative spatial curvature terms can be used to mimic radiation fluid and stiff matter. We conclude with some observations concerning future prospects.

Proposal for a New Quantum Theory of Gravity

Zeitschrift für Naturforschung A, 2019

We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of ...

Born's Reciprocal General Relativity Theory and Complex Non-Abelian Gravity as Gauge Theory of the Quaplectic Group: A Novel Path to Quantum Gravity (original) (raw)

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