Strict deformations of quantum field theory in de Sitter spacetime

Abstract

We show that a non-commutative structure arises naturally from perturbative quantum gravity in a de Sitter background metric. Our work builds on recent advances in the construction of observables in highly symmetric background spacetimes [Brunetti et al., JHEP 08, 032 (2016); Fröb and Lima, Class. Quant. Grav. 35, 095010 (2018)], where the dynamical coordinates that are needed in the relational approach were established for such backgrounds to all orders in perturbation theory. We show that these dynamical coordinates that describe events in the perturbed spacetime are naturally non-commuting, and determine their commutator to leading order in the Planck length. Our result generalizes the causal non-commutative structure that was found using the same approach in Minkowski space [Fröb, Much and Papadopoulos, Phys. Rev. D 107, 064041 (2023)].

Make Deformation Quantization Physical Again; Applications to QFT in Curved Spacetimes

“…Using the embedding formalism, analogously to [FM21], we define the Rieffel product as a smooth action of the the group R 4 , see [Rie93]. In this case, the smooth action α of R 4 acts as a translation in the embedding coordinates on functions extended to the embedding space.…”

“…While the deformed product is associative when defined at the same point, associativity does not hold if we define it for functions on different points. The reason for the dependence on the embedding point is given in detail for the de Sitter case in [FM21]. In particular, the smooth action α in Definition 2.4 is defined w.r.t.…”

“…These are defined in the coinciding point limit and in that limit the non-associative problem disappears. This choice is due to the approach taken in Minkowski ([GL07, GL08, BLS11], De-Sitter ( [FM21]) and the forthcoming results. Note that our approach is different from the one taken in [DLS20], where the underlying phase-space is quantized.…”

A deformation quantization for non-flat spacetimes and applications to QFT

“…Recently, this limitation was circumvented for the De Sitter spacetime by using the embedding formalism. The idea was to embed an n-dimensional CST manifold into a higher dimensional Minkowski spacetime, thus supplying us with an n-dimensional group of translations with which we define the Rieffel product, [FM21].…”