Abstract
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of dimensionally regularized $\phi^4$ theory in the minimal subtraction scheme up to seven loops.
Highlights
Quantum field theories (QFTs) are fundamental theories of physical interactions
Physical QFTs are the electroweak theory which combines electromagnetism with the weak interaction, quantum chromodynamics which describes the interaction between quarks and gluons, and φ4 theory for the Higgs boson
This is often done by generalizing to 4 − ε “dimensions”
Summary
Quantum field theories (QFTs) are fundamental theories of physical interactions. With the theory of graphical functions, a tool was developed to perform multiloop calculations in massless scalar field theories [7,8,9]. To make further contact to physics, it is necessary to regularize integrals which diverge in four dimensions This is often done by generalizing to 4 − ε “dimensions” (which can be defined in a parametric representation of QFT integrals [18]). Using GSVHs it was possible to obtain ε-expansions for QFT periods and graphical functions. The procedure Phi in HyperlogProcedures calculates the β-function and the anomalous dimensions γ and γm up to seven loops in the minimally subtracted OðnÞ symmetric φ4 theory [14].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
