Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Inductive definitions in logic versus programs of real-time cellular automata

Etienne Grandjean 1 Théo Grente 1 Véronique Terrier 1
1 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : Green functions in a quantum field theory can be expanded as bivariate series in the coupling and a scale parameter. The leading logs are given by the main diagonal of this expansion, i.e. the subseries where the coupling and the scale parameter appear to the same power; then the next-to leading logs are listed by the next diagonal of the expansion, where the power of the coupling is decremented by one, and so on. We give a general method for deriving explicit formulas and asymptotic estimates for any next-to k leading-log expansion for a large class of single scale Green functions. These Green functions are solutions to Dyson-Schwinger equations that are known by previous work to be expressible in terms of chord diagrams. We look in detail at the Green function for the fermion propagator in massless Yukawa theory as one example, and the Green function of the photon propagator in quantum electrodynamics as a second example, as well as giving general theorems. Our methods are combinatorial, but the consequences are physical, giving information on which terms dominate and on the dichotomy between gauge theories and other quantum field theories.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [45 references]  Display  Hide  Download
Contributor : Véronique Terrier <>
Submitted on : Tuesday, February 11, 2020 - 2:22:27 PM
Last modification on : Thursday, September 10, 2020 - 3:07:10 AM
Long-term archiving on: : Tuesday, May 12, 2020 - 2:43:48 PM


Files produced by the author(s)


  • HAL Id : hal-02474520, version 1


Etienne Grandjean, Théo Grente, Véronique Terrier. Inductive definitions in logic versus programs of real-time cellular automata. 2020. ⟨hal-02474520⟩



Record views


Files downloads