Gauge dependence and Dyson Schwinger equations II

• Applicant: Professor Dr. Dirk Kreimer
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Mathematics
• Term: from 2017 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 379766926

We aim at an understanding of gauge invariance in off-shell Green functions.Modern algebraic algebraic methods allow to attack the problem via the study of co-ideals in Hopf algebras. Green functions appear as solutions to fixed point equations in the Hochschild cohomology of these algebras and define in this manner the Dyson Schwinger equations. We concentrate our study on 4- and higher n-point functions, with external ghost-, gauge- and matter fields, in covariant linear and non-linear gauges and varying renormalization schemes. Using Lagrange multipliers such questions can also be studied for field theories in higher even dimensions and in the context of the operator product expansions.We will investigate universal properties across dimensions of such theories as suggested by the 1/N expansion, answering questions on relations to conformal field theory, the bootstrap and the a-Theorem.

• DFG Programme: Research Grants