Logarithms and deformation quantization

2014/01/14 by Alekseev, Anton, Rossi, Carlo A., Torossian, Charles +1
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1401.3200

Abstract

We prove the statement/conjecture of M. Kontsevich on the existence of the logarithmic formality morphism. This question was open since 1999, and the main obstacle was the presence of dr/r type singularities near the boundary r=0 in the integrals over compactified configuration spaces. The novelty of our approach is the use of local torus actions on configuration spaces of points in the upper half-plane. It gives rise to a version of Stokes' formula for differential forms with singularities at the boundary which implies the formality property. We also show that the logarithmic formality morphism admits a globalization from ℝ^d to an arbitrary smooth manifold.

Related

• Deformation Quantisation via Kontsevich Formality Theorem
• Deformation Quantization on ℝ^d
• Global logarithmic deformation theory
• Regularized integrals and manifolds with log corners
• Exactness, integrality, and log modifications