DFG Research Grant: Gauge Dependence and Dyson-Schwinger Equations

For gauge theories in particular we want to clarify the interplay between quantisation and gauge fixing in covariant gauges and the structure of (systems of) Dyson–Schwinger equations (DSE). We want to investigate this in the context of higher dimensional scalar field and gauge theories and for different renormalisation schemes. We focus on Wilson–Fisher fixed points at which the systems of DSEs become linear and hence scaling is reinstalled. This gives a possibility to classify the resulting sub-Hopf algebras, and we look forward to see if such an algebraic classification allows for a resulting classification of the underlying quantum field theories near and at their fixed point conformal limit.

For gauge theories in particular we want to clarify the interplay between quantisation and gauge fixing in covariant gauges and the structure of (systems of) Dyson–Schwinger equations (DSE). We want to investigate this in the context of higher dimensional scalar field and gauge theories and for different renormalisation schemes. We focus on Wilson–Fisher fixed points at which the systems of DSEs become linear and hence scaling is reinstalled. This gives a possibility to classify the resulting sub-Hopf algebras, and we look forward to see if such an algebraic classification allows for a resulting classification of the underlying quantum field theories near and at their fixed point conformal limit.

Duration of project

Start date: 10/2017

End date: 12/2019

Research Areas

Research Areas