On the mathematical sense of renormalization

Abstract

We place the renormalization procedure in quantum field theory into the familiar mathematical context of quantization of Poisson algebras. The Poisson algebra in question is the algebra of classical field theory Hamiltonians constructed in a previous paper (arXiv:1008.3333). Its quantum deformations presumably contain (non-canonically) the algebra of functional differential operators. We explain that this picture contains renormalization as a natural ingredient.

5 pages

References in corpus (1)

• The Poisson algebra of classical Hamiltonians in field theory and the problem of its quantization

Cited by in corpus (3)

• A new mathematical problem related to quantization of fields
• Differential operators on infinite dimensional space and quantum field theory
• A mathematical approach to quantum field theory