Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.

Gravitational Shielding Effect in Gauge Theory of Gravity

In 1992,E.E.Podkletnov and R.Nieminen found that under certain conditions,ceramic superconductor with composite structure reveals weak shielding properties against gravitational force.In classical Newton's theory of gravity and even in Einstein's general theory of gravity,there are no grounds of gravitational shielding effects.But in quantum gauge theory of gravity,the gravitational shielding effects can be explained in a simple and natural way.In quantum gauge theory of gravity,gravitational gauge interactions of complex scalar field can be formulated based on gauge principle.After spontaneous symmetry breaking,if the vacuum of the complex scalar field is not stable and uniform,there will be a mass term of gravitational gauge field.When gravitational gauge field propagates in this unstable vacuum of the complex scalar field,it will decays exponentially,which is the nature of gravitational shielding effects.The mechanism of gravitational shielding effects is studied in this paper,and some main properties of gravitational shielding effects are discussed.

Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.

The Gravity Gauge Theory and Gravity Field Equation in Flat Space

In this paper, we have proposed the theory of gravity gauge, and the gravity theory has been introduced into quantum field theory. We have further given the tensor equation of gravity field in the flat space, and found the gravity field equation is the Lorentz covariant and gauge invariant. The gravity theory can be quantized and can be unified with the electroweak and strong interaction at a new gauge group .

A New Solution with Torsion in Model of dS Gauge Theory of Gravity

A new static de Sitter solution with torsion in the model of de Sitter gauge theory of gravity is obtained. The torsion only contains Q（3）-symmetric tensor part according to irreducible decomposition. Some properties of the new solution are discussed.

Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge Theory

In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.

Unification of Gravitational and Electromagnetic Fields Using Gauge Symmetry

A new method for the unification of gravitational and electromagnetic forces is proposed. Previously, Kaluza-Klein theory dealt with the unification, but it has not yet been established as a complete theory. The main reason for this is that Kaluza-Klein theory has various contradictions due to the use of a 5-dimensional metric tensor. In this paper, unlike the conventional method, various equations related to gravitational and electromagnetic force are derived without any contradiction by processing equations having gauge symmetry within a 4-dimensional range. In this process, we propose that Maxwell’s equations for the electromagnetic force are expressed more simply and implicitly than the existing tensor form. Using the gauge symmetry, it shows that electromagnetic force can exist in single metric tensor along with gravity. In addition, since geodesic equations can be derived in the form of coordinate transformation, it has been shown that they are consistent with the existing equations. As a result, it has shown that they are consistent with the existing physical equations without contradiction.

Unification of Gravitational and Electromagnetic Fields in Curved Space-Time Using Gauge Symmetry of Bianchi Identities

This paper deals with the generalization of the linear theory of the unification of gravitational and electromagnetic fields using 4-dimensional gauge symmetry in order to solve the contradictions from the Kaluza-Klein theory’s unification of the gravitational and electromagnetic fields. The unification of gravitational and electromagnetic fields in curved space-time starts from the Bianchi identity, which is well known as a mathematical generalization of the gravitational equation, and by using the existing gauge symmetry condition, equations for the gravitational and electromagnetic fields can be obtained. In particular, the homogeneous Maxwell’s equation can be obtained from the first Bianchi identity, and the inhomogeneous Maxwell’s equation can be obtained from the second Bianchi identity by using Killing’s equation condition of the curved space-time. This paper demonstrates that gravitational and electromagnetic fields can be derived from one equation without contradiction even in curved space-time, thus proving that the 4-dimensional metric tensor using the gauge used for this unification is more complete. In addition, geodesic equations can also be derived in the form of coordinate transformation, showing that they are consistent with the existing equations, and as a result, they are consistent with the existing physical equations.

Gravitational Gauge Interactions of Dirac Field

Gravitational interactions of Dirac field are studied in this paper. Based on gauge principle, quantum gauge theory of gravity, which is perturbatively renormalizable, is formulated in the Minkowski space-time. In quantum gauge theory of gravity, gravity is treated as a kind of fundamental interactions, which is transmitted by gravitational gauge field, and Dirac field couples to gravitational field through gravitational gauge covariant derivative. Based on this theory, we can easily explain gravitational phase effect, which has already been detected by COW experiment.

Gauge Model with massive Gravitons

Gauge theory of gravity is formulated based on principle of local gauge invariance. Because the model hasstrict local gravitational gauge symmetry, and gauge theory of gravity is a perturbatively renormalizable quantum model.However, in the original model, all gauge gravitons are massless. We want to ask whether there exist massive gravitonsin Nature. In this paper, we will propose a gauge model with massive gravitons. The mass term of gravitational gaugefield is introduced into the theory without violating the strict local gravitational gauge symmetry. Massive gravitons canbe considered to be possible origin of dark energy and dark matter in the Universe.

Observation on Height Changes of Chinese Tide Gauges by GPS

The height changes of tide gauges directly influence sea level observation. For research of sea level variation in large region or globe, the land vertical displacement must be considered. Two sessions of GPS and absolute gravity observations in 2001 and 2003 are used to determine the horizontal and vertical motion of China coast in ITRF2000 and Eurasia frame. The difference between results of continuous observation and periodic observation is discussed.

Gauge Formulation of Heaviside’s Equations

A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside’s “linearized” equations are known as the “weak field approximation”. When derived from the primordial field equation, there is no mention of field strength;the assumption that the primordial field was predominant at the big bang rather suggests that ultra-strong fields are governed by the equations. This aspect has physical significance, so we explore the assumption by formulating the gauge field version of Heaviside’s theory. We compare with recent linearized gravity formulations and discuss the significance of differences.

The Unified Gauge Model of Four Interactions

We have reestablished the SU (5) grand unified model according to new research results in order to clarify some misunderstandings to the model. On this basis the unified gauge model describing four interactions containing gravity has been established, and its results are consistent with experiments.

General Relativity as the Classical Limit of the Renormalizable Gauge Theory of Volume Preserving Diffeomorphisms

The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an alternative approach to quantum gravity starts with the postulate that inertial energy-momentum and gravitational energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the quantum gauge field theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The classical limit of this theory coupled to a quantized scalar field is derived for an on-shell particle where inertial energy-momentum and gravitational energy-momentum coincide. In that process the symmetry under volume-preserving diffeomorphisms disappears and a new symmetry group emerges: the group of coordinate transformations of four-dimensional spacetime and with it General Relativity coupled to a classical relativistic point particle.

Proposal of a New Scalar Gauge in Relativity Field Equation

In this paper we propose a new gauge term in addition to the conventional gauge to acquire complete solution for the linear approximated gravitational equation. The calculation to make general form for the linear gravitational equation uses the well-known N?ether’s theorem saying that gauge symmetry is equal to conservation law. The unsolved coefficients in the equation require another condition which is leading to new gauge term. This proposed new gauge is a tensor product by a scalar quantity with a metric tensor having the trace value of 2. The scalar component in the 5th row and column of Kaluza-Klein’s metric tensor can be found as 2 diagonal components in our proposed 4×4 metric tensor. We also show that only a constant scalar gauge can be allowed in the curved space-time although arbitrary gauge can exist in the linear space-time.

Ashtekar-Kodama Gravity as a Classical and Quantum Extension of Loop Quantum Gravity

This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and in the quantum regime a full renormalizable quantum gauge field theory. The three fundamental constraints (hamiltonian, gaussian and diffeomorphism) were formulated in 3-dimensional spatial form within LQG in Ashtekar formulation using the notion of the Kodama state with positive cosmological constant Λ. We introduce a 4-dimensional covariant version of the 3-dimensional (spatial) hamiltonian, gaussian and diffeomorphism constraints of LQG. We obtain 32 partial differential equations for the 16 variables Emn (E-tensor, inverse densitized tetrad of the metric) and 16 variables Amn (A-tensor, gravitational wave tensor). We impose the boundary condition: for large distance the E-generated metric g(E) becomes the GR-metric g (normally Schwarzschild-spacetime). The theory based on these Ashtekar-Kodama (AK) equations, and called in the following Ashtekar-Kodama (AK-) gravity has the following properties. • For Λ = 0 the AK equations become Einstein equations, A-tensor is trivial (constant), and the E-generated metric g(E) is identical with the GR-metric g. • When the AK-equations are developed into a Λ-power series, the Λ-term yields a gravitational wave equation, which has only at least quadrupole wave solutions and becomes in the limit of large distance r the (normal electromagnetic) wave equation. • AK-gravity, as opposed to GR, has no singularity at the horizon: the singularity in the metric becomes a (very high) peak. • AK-gravity has a limit scale of the gravitational quantum region 39 μm, which emerges as the limit scale in the objective wave collapse theory of Gherardi-Rimini-Weber. In the quantum region, the AK-gravity becomes a quantum gauge theory (AK quantum gravity) with the Lie group extended SU(2) = ε-tensor-group(four generators) as gauge group and a corresponding covariant derivative. • AK quantum gravity is fully renormalizable, we derive its Lagrangian, which is dimensionally renormalizable, the normalized one-graviton wave function, the graviton propagator, and demonstrate the calculation of cross-section from Feynman diagrams.

Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schroedinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schroedinger equation, which can explain the gravitational phase effects found in COW experiments. And because of this Newtonian gravitational potential, a quantum particle in the earth＇s gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.

Scattering Cross-Sections in Quantum Gravity—The Case of Matter-Matter Scattering

Viewing gravitational energy-momentum PG<sup style='margin-left:-7px;'>μ as equal by observation, but different in essence from inertial energy-momentum PI<sup style='margin-left:-7px;'>μ naturally leads to the gauge theory of volume-preserving diffeomorphisms of a four-dimensional inner space. To analyse scattering in this theory, the gauge field is coupled to two Dirac fields with different masses. Based on a generalized LSZ reduction formula the S-matrix element for scattering of two Dirac particles in the gravitational limit and the corresponding scattering cross-section are calculated to leading order in perturbation theory. Taking the non-relativistic limit for one of the initial particles in the rest frame of the other the Rutherford-like cross-section of a non-relativistic particle scattering off an infinitely heavy scatterer calculated quantum mechanically in Newtonian gravity is recovered. This provides a non-trivial test of the gauge field theory of volume-preserving diffeomorphisms as a quantum theory of gravity.

<i>n</i>+ 1 Dimensional Gravity Duals to Quantum Criticalities with Spontaneous Symmetry Breaking

We reexamine the charged AdS domain wall solution to the Einstein-Abelian-Higgs model proposed by Gubser et al. as holographic superconductors at quantum critical points and comment on their statement about the uniqueness of gravity solutions. We generalize their explorations from 3 + 1 dimensions to arbitrary n + 1 Ds and find that the n + 1 ≥ 5D charged AdS domain walls are unstable against electric perturbations.

Surface growth approach for bulk reconstruction in the AdS/BCFT correspondence

In this study,we extend the surface growth approach for bulk reconstruction into the Ad S spacetime with a boundary in the Ad S/BCFT correspondence.We show that the geometry in the entanglement wedge with a boundary can be constructed from the direct growth of bulk extremal surfaces layer by layer.Furthermore,we observe that the surface growth configuration in BCFT can be connected with the defect multi scale entanglement renormalization ansatz(MERA)tensor network.Additionally,we investigate the entanglement of purification within the surface growth process,which not only reveals more refined structure of entanglement entropy in the entanglement wedge but also suggests a selection rule for surface growth in the bulk reconstruction.