Feynman diagrams of the unified theory at eleven parameters
Abstract
The unified theory of gravity and the Standard Model at eleven parameters is a Weylinvariant Lagrangian whose compensator is pure gauge and whose Lorentz connection and Weyl vector are algebraic. This paper writes its perturbative expansion in the Einstein gauge, the unitary gauge of the dilatation, and answers three questions: how the Standard Model is recovered, what the diagrams between the graviton and the other particles are, and where the theory stands with respect to the effective field theory of gravity, to asymptotic safety and to loop quantum gravity. The three fields without kinetic term are eliminated exactly: the connection into the axial four-fermion term of Hehl and Datta with the fixed coefficient 3πG/2; the Weyl vector and the trace of the torsion together into the kinetic coefficient of the Higgs, which corrects the one given in an earlier version of the unified paper and makes its Higgs inflation the Palatini one, with an unobservable tensor-to-scalar ratio; the compensator into the two masses ζM 2 P and y M M P . Every diagram made of Standard-Model lines keeps its expression; every graviton vertex carries √ 8π p, with p = p/(M P c) the dimensionless momentum of the eleven, so that the loop expansion is the ε-expansion of the kinematics. The graviton diagrams are those of the effective theory of gravity and are not renormalisable: the Higgs loop in the graviton self-energy is computed and generates C 2 and R 2 , the terms the design rule excluded, and the graviton's own loop, finite on shell at one loop, is set beside it with the two-loop term at which the finiteness ends. The four-fermion coefficient differs from the Immirzi-dependent one of loop quantum gravity by a factor nineteen, and the torsion bounce at twenty Planck densities is set beside loop quantum cosmology's at 0.41.
Related
- The unified theory at eleven parameters and the experiments: instrument by instrument, what is tested and what would refute
- Renormalisation of the unified theory at eleven parameters
- The new particle allowed by the unified theory at eleven parameters: the second doublet of the empty slot and where to look for it
- The unified theory at eleven parameters: general relativity and the Standard Model on one algebra
- The inverse of the algebraic element of the unified theory at eleven parameters, M 4 (C) ⊕ M 4 (H) ⊕ M 12 (C)
BibTeX
@misc{reynaud2026feynman,
title = {{Feynman diagrams of the unified theory at eleven parameters}},
author = {Patrick .B Reynaud},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05749764v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Feynman diagrams of the unified theory at eleven parameters
AU - Patrick .B Reynaud
PY - 2026
DA - 2026/09/14
PB - HAL
UR - https://hal.science/hal-05749764v2
AB - The unified theory of gravity and the Standard Model at eleven parameters is a Weylinvariant Lagrangian whose compensator is pure gauge and whose Lorentz connection and Weyl vector are algebraic. This paper writes its perturbative expansion in the Einstein gauge, the unitary gauge of the dilatation, and answers three questions: how the Standard Model is recovered, what the diagrams between the graviton and the other particles are, and where the theory stands with respect to the effective field theory of gravity, to asymptotic safety and to loop quantum gravity. The three fields without kinetic term are eliminated exactly: the connection into the axial four-fermion term of Hehl and Datta with the fixed coefficient 3πG/2; the Weyl vector and the trace of the torsion together into the kinetic coefficient of the Higgs, which corrects the one given in an earlier version of the unified paper and makes its Higgs inflation the Palatini one, with an unobservable tensor-to-scalar ratio; the compensator into the two masses ζM 2 P and y M M P . Every diagram made of Standard-Model lines keeps its expression; every graviton vertex carries √ 8π p, with p = p/(M P c) the dimensionless momentum of the eleven, so that the loop expansion is the ε-expansion of the kinematics. The graviton diagrams are those of the effective theory of gravity and are not renormalisable: the Higgs loop in the graviton self-energy is computed and generates C 2 and R 2 , the terms the design rule excluded, and the graviton's own loop, finite on shell at one loop, is set beside it with the two-loop term at which the finiteness ends. The four-fermion coefficient differs from the Immirzi-dependent one of loop quantum gravity by a factor nineteen, and the torsion bounce at twenty Planck densities is set beside loop quantum cosmology's at 0.41.
ER -