Graphical functions in QED and generalized single-valued hyperlogarithms in the f-alphabet
Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
Theoretical Condensed Matter Physics
Final Report Abstract
The DFG-project aimed to confirm my recently found connec- tion between motivic Galois theory in algebraic geometry and perturbative Quantum Field Theory (QFT). This goal was achieved beyond expectations and now this Galois-QFT link is a well established feature of both theories, known as the coaction principle. Very unexpectedly it was possible to extend the (now fully proved) theory to (firstly) all even dimensions ≥ 4 and (secondly) their deformations by a small ε > 0. The first breakthrough opened the door to new applications to six-dimensional φ3 QFT and eventually to Quantum Electrodynamics and Quantum Chromodynamisc. The second breakthrough made the transition to pure physics possible. With the deformation to non-integer dimensions it is possible to calculate full amplitudes in QFT which, by renormalization divergences, is not possible in pure integer dimensions. With these results, the calculation of renormalization functions (the QFT beta-function and the anomalous dimensions) could be calculated to a new record level. This landmark achievement had implications for the calcula- tion of critical exponents of phase transitions in various statistical models bridging to path from algebraic geometry to statistical physics.
Publications
- Numbers and functions in quantum field theory, Phys. Rev. D 97, 085018 (2016)
Oliver Schnetz
(See online at https://doi.org/10.1103/physrevd.97.085018) - The Galois coaction on the electron anomalous magnetic moment, Comm. in Number Theory and Physics 12, No. 2, 335–354 (2017)
Oliver Schnetz
(See online at https://doi.org/10.4310/cntp.2018.v12.n2.a4) - The Galois coaction on φ4 periods, Comm. in Number Theory and Physics 11, No. 3, 657–705 (2017)
Oliver Schnetz with E. Panzer
(See online at https://doi.org/10.4310/cntp.2017.v11.n3.a3) - Further investigations into the graph theory of φ4 -periods and the c2 -invariant (2018)
Oliver Schnetz with S. Hu, J. Shaw, K. Yeats
(See online at https://doi.org/10.48550/arXiv.1812.08751) - Closed strings as single-valued open strings: A genus-zero derivation, Journal of Physics A 52, No. 4, 045401 (2019)
Oliver Schnetz with O. Schlotterer
(See online at https://doi.org/10.1088/1751-8121/aaea14) - c2 invariants of Hourglass Chains via Quadratic Denominator Reduction, SIGMA 17, 100 (2021)
Oliver Schnetz with K.A. Yeats
(See online at https://doi.org/10.3842/sigma.2021.100) - Five-loop renormalization of φ3 theory with applications to the Lee-Yang edge singularity and percolation theory, Phys. Rev. D 103, No. 11, 116024 (2021)
Oliver Schnetz with M. Borinsky, J.A. Gracey, M.V. Kompaniets
(See online at https://doi.org/10.1103/physrevd.103.116024) - Geometries in perturbative quantum field theory, Comm. in Number Theory and Physics 15, No. 4, 743-791 (2021)
Oliver Schnetz
(See online at https://doi.org/10.4310/cntp.2021.v15.n4.a2)
