The two points of the quantum field are its important quantum properties. For space-time gravitational fields, if the space-time metric is considered as the basic field quantity of gravitation, then in the usual perturbation quantum gravitation, the two-point spreader of the metric field will play a role in determining the quantum nature of the gravitational field. For general relativity (GR), covariates can be normalized after subization; however, due to insurmountable dimensional difficulties, there has been no significant progress in the renormalization of multicyclic graphs.

However, in addition to the two-point propagator of the metric field in the gravitational field, the two points of contact and curvature can be established. All of them can be used to reveal the possible quantum properties of the gravitational field. For curvature, as it represents some kind of bending energy of the gravitational field, its correlation function and possible excitation have attracted people's attention. 1231. This paper has obtained the high derivative gravity and the harmony and coordinate of GR in any coordinate system. The gravitons under the system are free to propagate the manifestation of the child. Using the definition of the given two-point correlation function of spatio-temporal curvature, the specific results of the two-point vacuum correlation function for the four possible forms of curvature in high-index gravity are obtained through specific calculations. It is calculated that the curvature in GR cannot be propagated, but the curvature can be propagated in high-index gravity.

2 The graviton freely propagates into small quantum perturbations in the space-time background of MinkowSd. Its existence indicates that there is graviton propagation in the vacuum.

For space-time liaison, there will be an expansive expansion of the above formula by the magnitude of the perturbation h. In any coordinate system, using the normal generating functional method, the normal fixed term is taken in the quantized effective action as the usual notation. In this paper, the action of high-derivative gravity in the n-dimensional space-time M is taken as the free propagator of the gravitational space in the momentum space. 3. Definition of Curvature Vacuum Two-point Correlation Function In GR, there are several forms of curvature. This article uses the curvature vacuum two-point correlation function given in the four cases as the definition, that is, as above, D is the geodesic length from point x' to point x. U, is a tensor translational propagator, they are respectively defined as uf *, V (, x *) where the vector is flat 3 Uk () sequence operator of space-time manifold M. The perturbation calculation can be used to find the covariant and inverse translational propagators in the four arbitrary coordinate systems. Curvature Vacuum Two-Point Correlation Function In order to obtain the vacuum correlation function for several curvatures, we must first obtain the perturbation expansion of the curvature. For the Ricci curvature tensor, the h-order component is calculated and it is calculated that å©k has its h-order component for the curvature scalar, and the expansion is calculated for the Riemann curvature tensor, which is calculated as a 2h private 4.1.Riemann curvature. The correlation function of the quantity is substituted into formula (3) in equation (17). After perturbation, the formula (3) is based on the correlation function of 4.2Ricd tensor, which is the first term of h-magnitude expansion, and is substituted into formula (4). The first term of the (4) expansion is substituted for (5) for the correlation function (17) of the I 43 rotation matrix, and the first term of (5) is the substitution of d) into the above equation, which is summarized in this paper. In an exchangeable approximation, the formula (20) can be the same as the calculation of the Wilson loop around a dumbbell shaped closed loop.

44. Curvature scalar correlation function Substituting formula (16) into formula (6), after sorting, the first item of formula (6) is substituting d) into the above formula, and the result is 5. The curvature in the harmonic coordinate system Correlation Functions We have obtained the correlation functions of the four curvature forms in any coordinate system. If harmonic conditions are introduced, in the calculation and approximation of the perturbation in this paper, in the calculation of the curvature translation propagator and the use of path integration to obtain the free propagation agent of the graviton, the high-derivative graviton in the condition and coordinate system can be used. The free propagator is a quantized graviton propagator for GR. The other two terms are the propagators of the particles whose equivalent masses are Mi and M2, which are contributed by the square of the curvature, and can be similarly calculated to obtain the Rie-mann curvature tensor under the harmonic condition (22). The Ricci tensors, rotation matrices, and correlation functions for curvature scalars are substituting (3) into the above four equations, respectively, and the final expressions of the correlation functions for the four curvature forms will be obtained as well. The first terms of several curvature vacuum correlation functions obtained in the system and arbitrary coordinate systems are independent of the normative fixed parameter P used in the high-derivation prime powerization. Gravitational Propagator (2) Dynamic elimination.

In this high-derivative attraction action, as long as a = -2b = =0, the high-derivative attraction force becomes a GR attractive force. At this time, the graviton propagator (2) will change to --å£« + if the quantification of the GR is performed independently, and the fixed term of the quantizer specification is taken as r is the normative fixed parameter used when the GR is quantized. Then, similar path integral method can be used to obtain the free propagation of graviton as + if â€œthe graviton free spreads obtained by these two channels are the same.

The first terms (18), (19), (20), and (21) of the four functions of the gravitational curvature are transformed into a correlation function between the above results and the four curvatures obtained by self-quantization of GR. The same 151. The first terms of the functions GR*m, GR*GLP and GR all contain the derivative functions of 5 functions which are equal to zero. So the first contributions of these related functions are all zero. Higher-order and higher-order corrections may yield non-zero results, but they are low in number. Since the dimension of gravitational coupling constant k is ", it will lead to the failure of co-variable quantum gravity to be reformed. Under the quantification of Einstein's gravitation, higher-order and higher-order corrections appear to be inferior to the first one. The status is important, so in Einstein's gravitation, there is no vacuum correlation of two points of curvature.This conclusion obtained in this paper is consistent with the assumptions of many authors.Therefore, the curvature in GR does not have such quantum transition behavior.

However, the high-derivative gravity is different from that of GR. Since b Yin 0,c ping 0, the first terms (32), (33), (34), (35) of these curvature vacuum correlation functions are all non-zero. The contribution of higher order terms and higher order corrections to the correlation function will also not be zero. So for this gravitational force, due to the presence of nonlinear terms in the curvature of the Lagrangian, not only the high-derivative gravitational force is at least formally reformable, 61, but also the curvature can be propagated. This is a possible important quantum behavior of high-derivative gravity. The establishment of a non-zero curvature-related vacuum can be used to further explain the mechanism of gravitational interaction and explore the release and excitation of space-time energy.

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