Geometrically relating momentum cut-off and dimensional regularization

Abstract

The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the $\beta$-functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories.

As submitted to IJGMMP; International Journal of Geometric Methods in Mathematical Physics, 2013, Volume 10, Number 2

References in corpus (5)

• Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT
• Quantum fields and motives
• The Hopf algebra of Feynman graphs in QED
• A Perspective on Regularization and Curvature
• On matrix differential equations in the Hopf algebra of renormalization