NON-COMMUTATIVE COORDINATES FROM PERTURBATIVE QUANTUM GRAVITY

Speaker(s)

MARKUS B. FRÖB

Affiliation

Universität Leipzig, Germany

Language of the talk

English

Date

May 21, 2025, 5:15 p.m.

Information about the event

IMPAN 405 & ZOOM

Title in Polish

NON-COMMUTATIVE COORDINATES FROM PERTURBATIVE QUANTUM GRAVITY

Seminar

North Atlantic Noncommutative Geometry Seminar

---

Local observables in (perturbative) quantum gravity are notoriously hard to define, since the gauge symmetry of gravity (diffeomorphisms) moves points on the manifold. In particular, this is a problem for backgrounds of high symmetry such as the Minkowski spacetime, or the de Sitter spacetime which describes the early inflationary phase of our universe. Only recently, this obstacle has been overcome, and a field-dependent coordinate system has been constructed to all orders in perturbation theory in which observables are fully gauge invariant. I will explain the algebraic approach to perturbative quantum gravity, and show that these field-dependent coordinates are non-commutative, with an explicit expression for their commutator to the second order in the Planck length. This provides the first systematic derivation of non-commutativity that arises due to quantum-gravity effects. Based on joint work with A. Much and K. Papadopoulos.

 

---