KOINOT · COMPARATIVE VIEW

Ultraviolet infinities and quantum gravity

A comparison between the traditional ultraviolet problem of quantum field theory and the CTPA gravitational self-regularization program.

COMMON FORMAL PROBLEM

Perturbative quantum field theories generate loop integrals extending over arbitrarily high virtual momenta unless a physical high-energy limitation is supplied. In ordinary renormalizable theories this is handled through regularization and renormalization. Quantized general relativity, treated perturbatively in the conventional way, is not renormalizable by a finite set of parameters.

STANDARD / UNTIL NOW

Until now: the conventional view

Ultraviolet divergences are regularized mathematically and absorbed into renormalized parameters where the theory is renormalizable.
Until recently, in the conventional perturbative treatment, quantum general relativity required an ever-growing set of higher-order counterterms and was therefore regarded as a nonrenormalizable effective field theory at low energies.
The Planck scale is usually regarded as the scale where a new quantum-gravity description should become necessary, but standard perturbation theory itself does not supply a physical cutoff.

CTPA SOLUTION

CTPA solution: gravitational self-regularization

CTPA has recently proposed a resolution without introducing new physical hypotheses: one consistently applies established facts and the physical principles of general relativity and includes the external gravitational field of the high-energy virtual intermediate state itself rather than continuing flat-space loop kinematics to arbitrarily high energies.
As the total physical energy of the particle system in a localized virtual intermediate state approaches the Planck scale, its gravitational field becomes strong enough that local processes undergo gravitational freezing.
This produces a physical invariant ultraviolet boundary of order the Planck energy, so loop integrations do not extend to infinite energy.
With this Planck-scale cutoff the loop contributions are finite. In the CTPA program quantum gravity is therefore finite and practically renormalizable below the Planck scale: observable parameters are finite combinations of bare quantities and finite loop corrections.
At energies far below the Planck scale, direct residual quantum-gravitational effects are strongly suppressed.

Minimum formulas

Planck mass: M_P = √(ℏc/G).

Physical ultraviolet limit in the CTPA treatment: Λ ≈ M_P.

For E ≪ M_P, direct Planck-scale residuals are suppressed by powers of E/M_P.

STATUS

This is a CTPA research result and interpretation, not the present mainstream consensus. KOINOT presents it explicitly as the CTPA proposed resolution of the ultraviolet and perturbative quantum-gravity problem.