Noncommutative geometry and the BV formalism: application to a matrix model

Abstract

We analyze a U(2)-matrix model derived from a finite spectral triple. By applying the BV formalism, we find a general solution to the classical master equation. To describe the BV formalism in the context of noncommutative geometry, we define two finite spectral triples: the BV spectral triple and the BV auxiliary spectral triple. These are constructed from the gauge fields, ghost fields and anti-fields that enter the BV construction. We show that their fermionic actions add up precisely to the BV action. This approach allows for a geometric description of the ghost fields and their properties in terms of the BV spectral triple.

18 pages

References in corpus (4)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• An introduction to the Batalin-Vilkovisky formalism
• The BV formalism: theory and application to a matrix model
• BV-Quantization of a Noncommutative Yang-Mills Theory Toy Model

Cited by in corpus (6)

• From Noncommutative Geometry to Random Matrix Theory
• On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model
• One-loop corrections to the spectral action
• Batalin-Vilkovisky quantization of fuzzy field theories
• BV quantization of dynamical fuzzy spectral triples
• The loop equations for noncommutative geometries on quivers