The ultraviolet behavior of quantum Yang – Mills theory possess no instability as the separation between physical gluons becomes exceedingly smaller & smaller with increase in energy. Ultimately, at quantum length, in the limit of approaching the origin of field space, the dynamical variables, becomes so infinitesimal in magnitude that they effectively represent a single physical gluon G . At Gribov horizon, application of Gauss Divergence theorem to this single physical gluon G leads to singularities of color-Coulomb potential spread all over a spherical surface β at quantum length of physical gluon.
After acquiring additional degree of freedom in the form of free color-Coulomb potential at Gribov horizon, the gluon ‘G’ has the aforesaid spherical system β firmly attached to it. At Gribov horizon, the uncertainty principle forbids this spherical system β, of constant radius (h’/8π), to undergo any Lorentz – Fitzgerald contraction in laboratory inertial frame and rather, demands the motion of gluon ‘G’ to instantaneously drop to zero speed in the laboratory inertial reference frame. This sudden deceleration in the speed of gluon ‘G’ at Gribov horizon assigns an inertial mass to gluon ‘G’ in accordance with General Relativity theory. This inertial mass of gluon ‘G’ produces gravitational effect in its surroundings because of equivalence between inertial mass & gravitational mass in General Relativity theory.
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Preprint Mathematical Connection between Gravity and Standard Model
No, because the short distance behavior , i.e. the asymptotic freedom, of quantum Yang-Mills theory is found by assuming that spacetime is flat.
Yang-Mills theory is a field theory, that describes an indefinite number of particles; it's not a single particle theory.
Incidentally: A single gluon carries color charge, so is part of a multiplet of N^2-1 charges (if the gauge group is SU(N)).
The Gribov horizon is simply an expression of the fact that imposing the constraints that the gauge symmetry implies requires more than one chart on the manifold and a change of variables is required. In addition, it doesn't make sense focusing on quantities that aren't invariant under gauge transformations (like the potential).
Gluons are deconfined at short distances and they are massless particles as a consequence of gauge invariance. At longer distances they are confined into glueballs, that have a non-zero mass in a way that's known for many decades now. However this mass doesn't affect the spacetime geometry, since the scale where the strong interactions are relevant is orders of magnitude smaller than the scale where gravitational and quantum effects might have a chance of becoming comparable.
My humble submissions are as under,-
Everything is not alright in Yang – Mills theory. The quote of N. Christ (see Ref. 1 of my preprint) reads as under;-
“The two major physics discoveries of the first part of previous century, quantum mechanics and Einstein's theory of special relativity present new challenges when treated together. The energy "uncertainty" introduced in quantum theory combines with the mass-energy equivalence of special relativity to allow the creation of particle/anti-particle pairs by quantum fluctuations when the theories are merged. As a result, there is no self-consistent theory, which generalizes the simple, one-particle Schrodinger equation into a relativistic quantum wave equation.
The most successful approach to this problem, developed in the early 1930's, begins not with a single relativistic particle, but with a relativistic classical field theory, such as Maxwell's theory of electromagnetism. This classical field theory is then "quantized" in the usual way and the resulting quantum field theory realizes a consistent combination of quantum mechanics and relativity. However, this theory is inherently a many-body theory with the quanta of the normal modes of the classical field having all the properties of physical particles. The resulting many-particle theory can be relatively easily handled if the underlying field theory is essentially linear. Such is the case for the Maxwell theory where the photon field is essentially linear. However, the situation is completely reversed for the case of gluons that are the quanta of Yang–Mills field which obeys highly non-linear field equations. As a result, strong interaction physics has no known analytical approach.”
Further, the ‘’Yang – Mills and Mass-gap”” is one of the unsolved Claymath Millennium problems. As such, there is enough motivation for anyone to critically examine the currently accepted version of Yang – Mills theory. In other words, the statement “Yang-Mills theory is a field theory, that describes an indefinite number of particles; it's not a single particle theory.” can be challenged. While doing so in my preprint, the dynamic variables of the Yang - Mills theory have been simply redesignated as single particle variables in place of field variables and asymptotic freedom of Yang – Mills theory remains intact in single particle theory also because the single physical gluon still carries color charge as a source of asymptotic freedom and moreover, the flat space-time assumption of asymptotic freedom at short distance has not been abandoned in my preprint. The single particle interpretation of the dynamic variables of Yang – Mills theory is by definition inherently gauge invariant one for which any representative point in the field space (including Gribov horizon) is a physical state that allows one to focus on the quantities like the potential in gauge-invariant manner. The single particle interpretation being inherently gauge-invariant automatically lend itself to deconfinement and massless nature at short distances. At large distances, there is no experimental confirmation of existence of non-massless glueballs as an explanation for confinement of gluons. This implies that there is room for the single particle interpretation to offer following alternate explanation for mass-gap and confinement at Gribov horizon physical state.
The quantization of uncertainty in linear momentum of the single physical gluon G leads to spherical surface at the quantum length of the said single physical gluon G such that at Gribov horizon physical state, this spherical surface firmly gets attached to physical gluon G due to increase in its degrees of freedom. At Gribov horizon, the uncertainty principle forbids this spherical system β, of constant planck constant radius (h’/8π), to undergo any Lorentz – Fitzgerald contraction in laboratory inertial frame and rather, demands the motion of gluon ‘G’ to instantaneously drop to zero speed in the laboratory inertial reference frame. This sudden deceleration in the speed of gluon ‘G’ at Gribov horizon assigns an inertial mass to gluon ‘G’ in accordance with General Relativity theory. This inertial mass of gluon ‘G’ produces gravitational effect in its surroundings because of equivalence between inertial mass & gravitational mass in General Relativity theory.
N. Christ's comments don't have anything to do with the question asked, though. That Yang-Mills theory has a mass gap doesn't mean that the gluons acquire a mass; it means that there don't exist states with masses smaller than a particular finite value. Indeed, since at long distances Yang-Mills describes confined gluons, these don't appear in the spectrum at all. So it isn't true that gluons acquire a mass, but that glueballs can't be massless.
And gravitational effects are irrelevant because the energy scale where glueballs form is orders of magnitude smaller from the scale where gravity might be relevant.
N Christ comments were included to highlight the incompleteness of Yang Mills theory as on date and the fact that single particle interpretation cannot be outwrightly rejected. The mass-gap of Yang - Mills theory lacks clear cut explanation as on date and as such, the gluons can also acquire mass at Gribov horizon physical state till the arguments offered in support of the same are falsified on some other valid theoretical grounds. Glueballs have not been experimentally confirmed till date, so, massive gluon at Gribov horizon physical state still holds ground until the offered Single particle theory for the same is logically rejected. Gravitational effects are relevant because the same have been included by logically combining GR and QM at the quantum length of Physical gluon where the strong force merges into gravitational force at Gribov horizon.
quantum Yang-Mills is asymptotically free, hence has a trivial UV fixed point.
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