# Dynkin operators, renormalization and the geometric $\beta$ function

@article{Agarwala2012DynkinOR, title={Dynkin operators, renormalization and the geometric \$\beta\$ function}, author={Susama Agarwala}, journal={arXiv: Mathematical Physics}, year={2012} }

In this paper, I show a close connection between renormalization and a generalization of the Dynkin operator in terms of logarithmic derivations. The geometric $\beta$ function, which describes the dependence of a Quantum Field Theory on an energy scale defines is defined by a complete vector field on a Lie group $G$ defined by a QFT. It also defines a generalized Dynkin operator.

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 12 REFERENCES

Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group

- Physics, Mathematics
- 2001

- 319
- PDF

The geometric $\beta$-function in curved space-time under operator regularization

- Mathematics, Physics
- 2009

- 2
- PDF

Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

- Physics, Mathematics
- 2000

- 442
- PDF

On matrix differential equations in the Hopf algebra of renormalization

- Mathematics, Physics
- 2006

- 17
- PDF

Renormalization in quantum field theory and the Riemann- Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem

- Mathematics
- 2007

- 209
- Highly Influential