Quantum gravity

Beta function (physics)

Physics

Renormalization

Field theory (psychology)

Pure mathematics

Mathematics

Mathematical physics

Quantum field theory

Mathematical analysis

Thermal quantum field theory

Relationship between string theory and quantum field theory

Theoretical physics

Quantum mechanics

Subtraction

Scheme (mathematics)

Field (mathematics)

Quantum

Arithmetic

Physical review. D/Physical review. D.

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.

Numbers and functions in quantum field theory