BPHZ renormalization and its application to non-commutative field theory

Abstract

In a recent work a modified BPHZ scheme has been introduced and applied to one-loop Feynman graphs in non-commutative phi^4-theory. In the present paper, we first review the BPHZ method and then we apply the modified BPHZ scheme as well as Zimmermann's forest formula to the sunrise graph, i.e. a typical higher-loop graph involving overlapping divergences. Furthermore, we show that the application of the modified BPHZ scheme to the IR-singularities appearing in non-planar graphs (UV/IR mixing problem) leads to the introduction of a 1/p^2 term and thereby to a renormalizable model. Finally, we address the application of this approach to gauge field theories.

27 pages, 4 figures; v2 references added, to appear in EPJC

References in corpus (8)

• Noncommutative Induced Gauge Theory
• A translation-invariant renormalizable non-commutative scalar model
• Induced Gauge Theory on a Noncommutative Space
• Gribov horizon beyond the Landau gauge
• One-Loop Calculations for a Translation Invariant Non-Commutative Gauge Model
• Translation-invariant models for non-commutative gauge fields
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• On the Renormalization of Non-Commutative Field Theories

Cited by in corpus (6)

• Ultraviolet-complete quantum field theories with fractional operators
• The Gribov problem in Noncommutative gauge theory
• Aspects of perturbative quantum field theory on non-commutative spaces
• Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme
• Gauge Fields on Non-Commutative Spaces and Renormalization
• The BPHZL renormalization of a planar quantum electrodynamics up to 2-loops and beyond