Schwinger-Dyson Equations in Group Field Theories of Quantum Gravity
Mathematical Physics
2012-11-07 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
In this talk, we elaborate on the operation of graph contraction introduced by Gurau in his study of the Schwinger-Dyson equations. After a brief review of colored tensor models, we identify the Lie algebra appearing in the Schwinger-Dyson equations as a Lie algebra associated to a Hopf algebra of the Connes-Kreimer type. Then, we show how this operation also leads to an analogue of the Wilsonian flow for the effective action. Finally, we sketch how this formalism may be adapted to group field theories.
Keywords
Cite
@article{arxiv.1211.1244,
title = {Schwinger-Dyson Equations in Group Field Theories of Quantum Gravity},
author = {Thomas Krajewski},
journal= {arXiv preprint arXiv:1211.1244},
year = {2012}
}
Comments
talk given at "The XXIX International Colloquium on Group-Theoretical Methods in Physics", Chern Institute of Mathematics August 2012, submitted to the conference proceedings