On the phenomenological three-graviton vertex
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the Phenomenological Three-Graviton Vertex A. I. Nikishov Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia e-mail: [email protected] Abstract—In General Relativity, the graviton interacts in three-graviton vertex with a tensor that is not the energy–momentum tensor of the gravitational field. We consider the possibility that the graviton interacts with the definite gravitational energy–momentum tensor that we previously found in the G2 approximation. This tensor in a gauge, where nonphysical degrees of freedom do not contribute, is remarkable, because it gives positive gravitational energy density for the Newtonian center in the same manner as the electromagnetic energy–momentum tensor does for the Coulomb center. We show that the assumed three-graviton vertex does not lead to contradiction with the precession of Mercury’s perihelion. In the S-matrix approach used here, the external gravitational field has only a subsidiary role, similar to the external field in quantum electrodynamics. This approach with the assumed vertex leads to the gravitational field that cannot be obtained from a consistent gravity equation. PACS numbers: 04.20.Fy DOI: 10.1134/S1063779606050042
1. INTRODUCTION The field-theoretical approach to gravitation brings complementary understanding both within and beyond the bounds of General Relativity. For example, this approach gives a glimpse to find the gµν of the privileged reference frame, which is free from the contribution of the unphysical field degrees of freedom, distorting the properties of a correctly chosen gravitational energy–momentum tensor. From the general point of view, it is also desirable to have the frame of reference reflecting metric properties due to gravitation, but free of features originating from the possibility of arbitrary choice of the coordinate system. The Schwarzschild solution in General Relativity could be represented in different equivalent forms: standard, isotropic, harmonic, and others. (The Schwarzschild solution is usually presented in the standard form according to Weinberg terminology [1].) After the field is switched off, all three forms named go over to the one Cartesian coordinate system (for the sake of definiteness). Under the turned-on weak field, the harmonic and isotropic systems are indicative of the gravitational field still retaining spatial isotropy. On the contrary, the standard Schwarzschild system suggests that such isotropy does not exist [2, 3]. In General Relativity, the problem of the relationship of coordinates in gµν with the laboratory coordinates can be solved only after the fulfillment of a complicated procedure (conceptually possible) (see Sect. 23.3 in [4]). The field-theoretical approach offers supplementary possibilities. Preference is given to isotropy [5]. Actually, imposition of the Hilbert gauge condition [5], or harmonicity condition [6] (in a weak field, these conditions coincide with each other) leads to isotropy. But in
formation of the standard system, the unphysical degrees of freedom are involv
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