Gauge Model Based on Group G×SU（2）

We present a model of gauge theory based on the symmetry group G×SU（2） where G is the gravitational gauge group and SU（2） is the internal group of symmetry. We employ the spacetime of four-dimensional Minkowski, endowed with spherical coordinates, and describe the gauge fields by gauge potentials. The corresponding strength field tensors are calculated and the field equations are written. A solution of these equations is obtained for the case that the gauge potentials have a particular form potentials induces a metric of Schwarzschild type on with spherical symmetry. The solution for the gravitational the gravitational gauge group space.     

Reissner--Nordström-de--Sitter-type Solution by a Gauge Theory of Gravity

We use the theory based on a gravitational gauge group （Wu＇s model） to obtain a spherical symmetric solution of the field equations for the gravitational potential on a Minkowski spacetime. The gauge group, the gauge covariant derivative, the strength tensor of the gauge feld, the gauge invariant Lagrangean with the cosmological constant, the field equations of the gauge potentiaIs with a gravitational energy-momentum tensor as well as with a tensor of the field of a point like source are determined. Finally, a Reissner-Nordstrom-de Sitter-type metric on the gauge group space is obtained.     

Gauge Gravitational Field in a Fractal Space-Time

Considering the fractal structure of space-time, the scale relativity theory in the topological dimension D_T=2 is built. In such a conjecture, the geodesics of this space-time imply the hydrodynamic model of the quantum mechanics. Subsequently, the gauge gravitational field on a fractal space-time is given. Then, the gauge group, the gauge-covariant derivative, the strength tensor of the gauge field, the gauge-invariant Lagrangean, the field equations of the gauge potentials and the gauge energy-momentum tensor are determined. Finally, using this model, a Reissner-Nordström type metric is obtained.     

Hamiltonian treatment of the spherically symmetric einstein-Yang-Mills system

A canonical formalism of the dynamics of interacting spherically symmetric Yang-Mills and gravitational fields is presented. The work is based on Dirac's technique for constrained hamiltonian systems. The gauge freedom of the Yang-Mills field is treated in the same footing with the coordinate transformation freedom of the gravitational field. In particular, the fixation of coordinates and the fixation of the internal gauge are achieved by totally similar techniques. Two classes of spherically symmetric motions are considered: (i) the class for which the Yang-Mills potentials themselves are spherically symmetric (“manifest spherical symmetry”). In this case the results are valid for an arbitrary gauge group; and (ii) the class for which, in the SO(3) gauge group, a rotation in physical space is compensated by a rotation of equal magnitude but opposite direction in isospin space (“spherical symmetry up to a gauge transformation”). For manifest spherical symmetry the problem amounts to effectively dealing with an abelian gauge group and the most general solution of the field equations turns out to be the Reissner-Nordström metric with a Coulomb field. For spherical symmetry up to a gauge transformation the problem is more interesting. the formalism contains then, besides the gravitational variables, three pairs of functions of the radial coordinate that describe the degrees of freedom of the Yang-Mills field. Two pairs of these functions can be combined into a complex field ψ and its conjugate. The hamiltonian is then invariant under r-dependent rotations in the complex ψ-plane. The third degree of freedom plays the role of a compensating field associated with this invariance under localized U(l) rotations. The compensating field can always be brought to zero by a gauge transformation. After this is done the gauge is completely fixed but the problem remains invariant under position independent rotations in the ψ plane. Static solutions of the field equations in this gauge are of the form ψ(r) = (r) exp (iΘ) with Θ independent of position. The particular case Θ = 0 corresponds to the Wu-Yang ansatz. A nontrivial static solution can be found in closed form. The Yang-Mills field is of the generalized Wu-Yang type with an extra electric term, and the metric is the Reissner-Nordström one. It is pointed out that a Higgs field can be easily introduced in the formalism. The addition of the Higgs field does not destroy the invariance of the Hamiltonian under r-dependent rotations in the ψ-plane. The conserved quantity associated with the invariance under ψ → exp (i(const))ψ coincides with the electric charge as defined by 't Hooft in a more general context.     

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.     

Self-dual monopoles and toda molecules

Stable static solutions to a gauge field theory with a Higgs field in the adjoint representation and with vanishing self-coupling are self-dual in the sense of Bogomolny. Leznov and Saveliev showed that a specific form of spherical symmetry reduces these equations to a modified form of the Toda molecule equations associated with the overall gauge symmetry G. Values of the constants of integration are found in terms of the distant Higgs field, guaranteeing regularity of the solution at the origin. The expressions hold for any simple Lie group G, depending on G via its root system.     

Gauge fields and gravitational field equations

It is shown that the gravitational field equations in free space have a similar form to the free Yang-Mills field equations, where the group SL (2, C) replaces the group SU(2). The Ricci rotation coefficients take the role of the Yang-Mills like potentials, whereas the Riemann tensor takes the role of the gauge fields.     

Cosmological Model Based on Gauge Theory of Gravity

A cosmological model based on gauge theory of gravity is proposed in this paper. Combining cosmological principle and field equation of gravitational gauge field, dynamical equations of the scale factor R(t) of our universe can be obtained. This set of equations has three different solutions. A prediction of the present model is that, if the energy density of the universe is not zero and the universe is expanding, the universe must be space-flat, the total energy density must be the critical density ρ_c of the universe. For space-flat case, this model gives the same solution as that of the Friedmann model. In other words, though they have different dynamics of gravitational interactions, general relativity and gauge theory of gravity give the same cosmological model.     

Solution of Maxwell’s equations on a de Sitter background

The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space–time studied in static spherical coordinates. There is no source besides the background. One component of the vector field is expressed, in its radial part, through the solution of a fourth-order ordinary differential equation obeying given initial conditions. The other components of the vector field are then found by acting with lower-order differential operators on the solution of the fourth-order equation (while the transverse part is decoupled and solved exactly from the beginning). The whole four-vector potential is eventually expressed through hypergeometric functions and spherical harmonics. Its radial part is plotted for given choices of initial conditions. We have thus completely succeeded in solving the homogeneous vector wave equation for Maxwell theory in the Lorenz gauge when a de Sitter space–time is considered, which is relevant both for inflationary cosmology and gravitational wave theory. The decoupling technique and analytic formulae and plots are completely original. This is an important step towards solving exactly the tensor wave equation in de Sitter space–time, which has important applications to the theory of gravitational waves about curved backgrounds.     

The Standard Model with Higgs as Gauge Field on Fourth Homotopy Group

Based upon a fundamental principle, the generalized gauge principle, we construct a general model with G_L×G'_R×Z₂ gauge symmetry, where Z₂ = π₄(G_L) is the fourth homotopy group of the gauge group G_L, by means of the non-commutative differential geometry and reformulating the standard model with the Higgs field being a gauge field on the fourth homotopy group of their gauge groups. We show that in this approach not only the Higgs field is automatically introduced on an equal footing with ordinary Yang-Mills gauge potentials and there are no extra constraints among the parameters at the tree level but also most importantly the models survive quantum corrections.     

A Review About Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry

In this review paper, we discuss how gravity and spin can be obtained as the realization of the local Conformal-Affine group of symmetry transformations. In particular, we show how gravitation is a gauge theory which can be obtained starting from some local invariance as the Poincaré local symmetry. We review previous results where the inhomogeneous connection coefficients, transforming under the Lorentz group, give rise to gravitational gauge potentials which can be used to define covariant derivatives accommodating minimal couplings of matter, gauge fields (and then spin connections). After we show, in a self-contained approach, how the tetrads and the Lorentz group can be used to induce the spacetime metric and then the Invariance Induced Gravity can be directly obtained both in holonomic and anholonomic pictures. Besides, we show how tensor valued connection forms act as auxiliary dynamical fields associated with the dilation, special conformal and deformation (shear) degrees of freedom, inherent to the bundle manifold. As a result, this allows to determine the bundle curvature of the theory and then to construct boundary topological invariants which give rise to a prototype (source free) gravitational Lagrangian. Finally, the Bianchi identities, the covariant field equations and the gauge currents are obtained determining completely the dynamics.     

SPHERICALLY SYMMETRIC AND STATIC FIELDS IN LINEARIZED GAUGE THEORIES OF GRAVITATION

In this paper Newtonian limit in the Poincare gauge field theory of gravitation is investigated. In spherically symmetric and static cases interior and exterior solutions of the linearized field equations with gravitational sourtion are obtained by maens of Green's function for the five Lagrangians with out ghosts and tachyons. In cases of four Lagrangians,the space-time metrics outside gravitational source are the usual Schwarzschild one of the first-older, while in the case of the fifth hagrangian the space-time metric differs from the Schwarzschild one. Under both,Newtonian and-weak gravitational field approximations,the motion of a test particle without span should therefore be different from Newton's second law. As a result of the exchanged particles of spin o⁺ the deviation from Newton's second law is a Yukawa term which is attractive. A distance-dependent gravitational "constant" G(r) can be defined according to the new result. The difference between G(r) and Newton's gravitational constant G_∞ is due to a nonzero component of torsion tensor, the effect of which can be tested by measuring G(r).     

Gravitation and unified covariant formalism of classical gauge fields in equiaffine space

In this paper, we construct a unified covariant formalism for the classical gauge fields in an equiaffine space. The gauge transformation groups are the Lie groups, induced according to the third Lie theorem by the structure constants. As a result of the gauge transformations, one set of geometric objects is replaced by another. It is confirmed that the differential conservation laws in the equiaffine spaces are a result of the equations of the gauge fields. The particular case when the gauge transformation group is a four-parameter group and is abelian is distinguished. This group corresponds to gauge fields that are induced by an energy-momentum tensor and, which, as a result, are called gravitational fields. As a particular case of the equations of the given gravitational fields, we obtain Einstein's equations with the help of a Lagrangian, which is quadratic with respect to the gravitational field intensities. In concluding, we note the possibility of describing gauge fields, corresponding to nongravitational interactions of vector mesons with nonzero rest mass, without invoking the scalar Higgs mesons. This possibility appears both as a result of the generalization of the Yang-Mills covariant derivative and as a result of including gravitational interactions in the general gauge field formalism.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 12, 47–51, December, 1981.     

关于动态位错场张量势的规范变换

本文引入并论证了描述动态位错场的张量势(A与B)的规范交换问题,而且证明这种变换可采取这样的形式:B′=B+▽F, A′=A-ρ?/(?t)▽G,x′=x-ρ?/(?t)F,其中x_i=e_iklA_kl。至于F与G,则为带有很大任意性的时空坐标的矢量函数,但它们要满足以下关系式:F=▽×G,▽²F-1/G_t²-(?²/?t²)F=0.进 关键词：     

General relativistic axisymmetric rotating systems: Coordinates and equations

The Einstein equations for rotating axisymmetric configurations in asymptotically flat spacetimes are put in a form suitable for numerical calculations of dynamics. The discussion is motivated by the astrophysical problem of gravitational collapse with generation of gravitational radiation and possibly black hole formation. In the context of topologically spherical coordinates there are two spatial gauge conditions which greatly simplify the Einstein equations and are compatible with regularity at the origin. We focus on one, the radial gauge, which generalizes Schwarzschild coordinates and is asymptotically a transverse-traceless gauge for gravitational radiation. The shift vector equation and the Hamiltonian constraint are parabolic equations in the radial gauge, rather than the usual elliptic equations. Two hypersurface conditions are explored in detail, the maximal hypersurface condition and another “polar” hypersurface condition which fits naturally with the radial gauge.     

Spherical conformal models for compact stars

We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass–radius limit and the surface red shift are consistent with observational constraints.     

Analytic solution of gauge field equations for Lorentz gravity

The exterior analytic solution for a static, spherically symmetric system is given by means of a set of gauge field equations from Lorentz gravity in the curvature coordinate. The correction contributed by the gravitational gauge field in the exterior of a static sphere is obtained for the gravity.