I'm working on the variation of strong coupling constant with respect to the time, where the coupling constant of QCD " g" defined as g= g_0 \epsilon (t) ,
can we take non minimall coupling between \epsilon and the Recci scalar, where \epsilon is dimensionless field while the non minimal coupling is taken with the scalar field which have "M_p_l unite"?
If you have figured out what gravity means, then you also know the answer. The gravitation potential reflects the influence that massive particles have on the space in which we live. Thus, the most convenient interpretation of this situation is that the space in which we live can be represented by a field (NOT THE EM FIELD !!!) and that the gravitation potential is no more and no less than a smoothed version of this field. The "space field" is contracted by the influence of point-like particles that obstruct the continuity of this field. A coherent swarm of such obstructions causes a smooth contraction in the smoothed version of the field. The number of elements in the swarm and the spread of the swarm are characteristics of the impact that the swarm has on the deformation of the field. A Gaussian distribution of the obstructions would result in a smoothed shape that is described by ERF(r)/r. At some larger distance r this behaves as 1/r. The spread of the Gaussian distribution and the number of contributing obstructions determine the impact of the swarm.
http://www.e-physics.eu/TheHilbertBookTestModel.pdf
Why not? E.g. one can multiply the Lagrangian by arbitrary scal function of scalar curvature.
UNIFICATION of GRAVITATION and ELECTROMAGNETISM
I unified at Quantum level, Electromagnetism and Gravitation with Ferent equation for the energy of a photon:
E = h × f + a × f
Ferent equation for photon – graviton interaction:
E = h × f + a × f - a × ν
where - a × ν is the negative energy of the graviton
ν is the frequency of the graviton
“I am the first who understood and explained Gravitation with high speed gravitons v = 1.001762 × 10^17 m/s, with Negative Momentum, Negative Mass and Negative Energy” Adrian Ferent
https://www.researchgate.net/publication/299135595_Ferent_Gravitation_theory
Article Ferent Gravitation theory
As espilon (t) is dimensionless while the Ricci scalar has a dimension 1/(length)^2, you would need another dimensional coupling constant to multiply the nonminimal coupling to create an interaction Lagrangian density consisting of espilon (t) and the Ricci scalar which has the dimension= Energy/(length)^3.
Yes, it is possible and nonminimal couplings appear recently quite frequently in various theories. As Das Gupta says, it is necessary to introduce an additional dimensional constant. The problem is that nonminimal couplings may be arbitrary and it is hard to guess the correct one. General relativity assumes minimal couplings and interactions must be defined first in the framework of special relativity. As far as I know up to now no nonminimal coupling fits well the physical world. And why does the $\epsilon$ depend solely on time? This is noncovariant and contradicts the very idea of general relativity. Even if in some distinguished frame this is only a function of $t$,
the interaction term in the Lagrangian must have a covariant form and be a scalar.
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