Graviton Fields Under Helicity Rotations. Thought of the Day 156.0

Einstein described gravity as equivalent to curves in space and time, but physicists have long searched for a theory of gravitons, its putative quantum-scale source. Though gravitons are individually too weak to detect, most physicists believe the particles roam the quantum realm in droves, and that their behavior somehow collectively gives rise to the macroscopic force of gravity, just as light is a macroscopic effect of particles called photons. But every proposed theory of how gravity particles might behave faces the same problem: upon close inspection, it doesn’t make mathematical sense. Calculations of graviton interactions might seem to work at first, but when physicists attempt to make them more exact, they yield gibberish – an answer of “infinity.” This is the disease of quantized gravity. With regard to the exchange particles concept in the quantum electrodynamics theory and the existence of graviton, let’s consider a photon that is falling in the gravitational field, and revert back to the behavior of a photon in the gravitational field. But when we define the graviton relative to the photon, it is necessary to explain the properties and behavior of photon in the gravitational field. The fields around a “ray of light” are electromagnetic waves, not static fields. The electromagnetic field generated by a photon is much stronger than the associated gravitational field. When a photon is falling in the gravitational field, it goes from a low layer to a higher layer density of gravitons. We should assume that the graviton is not a solid sphere without any considerable effect. Graviton carries gravity force, so it is absorbable by other gravitons; in general; gravitons absorb each other and combine. This new view on graviton shows, identities of graviton changes, in fact it has mass with changeable spin.

When we derive various supermultiplets of states, at the noninteracting level, these states can easily be described in terms of local fields. But, at the interacting level, there are certain ambiguities that withdraw as a result of different field representations describing the same massless free states. So the proper choice of the field representation may be subtle. The supermultiplets can then be converted into supersymmetric actions, quadratic in the fields. For selfdual tensor fields, the action must be augmented by a duality constraint on the corresponding field strength. For the graviton field,

The linearized Einstein equation for g_μν = η_μν + κh_μν implies that (for D ≥ 3)

R_μν ∝ ∂²h_μν + ∂_μ∂_νh – ∂_μ∂^ρh_νρ – ∂_ν∂^ρh_ρμ = 0 —– (1)

where h ≡ h_μμ and R_μν is the Ricci tensor. To analyze the number of states implied by this equation, one may count the number of plane-wave solutions with given momentum q^μ. It then turns out that there are D arbitrary solutions, corresponding to the linearized gauge invariance h_μν → h_μν + ∂_μξ_ν + ∂_νξ_μ, which can be discarded. Many other components vanish and the only nonvanishing ones require the momentum to be lightlike. Thee reside in the fields h_ij, where the components i, j are in the transverse (D-2) dimensional subspace. In addition, the trace of h_ij must be zero. Hence, the relevant plane-wave solutions are massless and have polarizations (helicities) characterized by a symmetric traceless 2-rank tensor. This tensor comprises 1/2D(D-3), which transform irreducibly under the SO(D-2) helicity group of transverse rotations. For the special case of D = 6 spacetime dimensions, the helicity group is SO(4), which factorizes into two SU(2) groups. The symmetric traceless representation then transforms as a doublet under each of the SU(2) factors and it is thus denoted by (2,2). As for D = 3, there are obviously no dynamic degrees of freedom associated with the gravitational field. When D = 2 there are again no dynamic degrees of freedom, but here (1) should be replaced by R_μν = 1/2g_μνR.

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