arXiv subjects

Valentine Maris

Publications and source records attributed to Valentine Maris.

6 recordsLinked to original sources

arXiv2026

Les Houches lectures on Spinfoam Path Integrals

In these lecture notes for the Les Houches School on Loop Quantum Gravity 2025, which took place in September 2025, we give a pedagogical review of the basics of the spinfoam framework for a quantum gravity path integral. While spin network states in loop quantum gravity describe the quantum geometry of the 3d space as dynamical networks of entangled quanta of volumes, spinfoams define transition amplitudes for those spin networks using the reformulation of general relativity as an "almost-topological" field theory and tools from quantum BF theory and topological state-sums. The lectures were a short format of three times one hour and a half, only allowing to cover the basics and offer a glimpse of more advanced lines of research. We introduce spin foam path integrals for increasing spacetime dimensions starting with 2d BF theory, then build up to 3d quantum gravity with the Ponzano-Regge state-sum and the Turaev-Viro invariant, and finally the quantization of general relativity in four dimensions.

gr-qc↗

arXiv2025

Quantum causality in kappa Minkoswki

Recent results on causality in noncommutative space-time are reviewed. We study, in particular, quantum causal structures in 1+1 dimensional kappa Minkowski space-time. This later is described by a twisted Lorentzian Spectral Triple build with a twisted set of derivatives. Investigation of causality provides a quantum constraint, which is a quantum analog of the speed light limits

hep-th↗

arXiv2025

Star-products for Lie-algebraic noncommutative Minkowski space-times

Poisson structures of the Poincar\'e group can be linked to deformations of the Minkowski space-time, classified some time ago by Zakrewski. Based on this classification, various quantum Minkowski space-times with coordinates Lie algebras and specific Poincare Hopf algebras have been exhibited by Mercati and called T-Minkowski space-times. Here we construct the star products and involutions characterizing the $\star$-algebras for a broad family of Lie algebras which includes 11 out of 17 Lie algebras of T-Minkowski spaces. We show that the usual Lebesgue integral defines either a trace or a KMS weight ('twisted trace') depending on whether the Lie group of the coordinates' Lie algebra is unimodular or not. Finally, we give the Poincar\'e Hopf algebras when they are compatible with our $*$-product. General derivation of such symmetry Hopf algebras are briefly discussed.

hep-th↗

arXiv2024

Gauge theory on $ρ$-Minkowski space-time

We construct a gauge theory model on the 4-dimensional $ρ$-Minkowski space-time, a particular deformation of the Minkowski space-time recently considered. The corresponding star product results from a combination of Weyl quantization map and properties of the convolution algebra of the special Euclidean group. We use noncommutative differential calculi based on twisted derivations together with a twisted notion of noncommutative connection. The twisted derivations pertain to the Hopf algebra of $ρ$-deformed translations, a Hopf subalgebra of the $ρ$-deformed Poincaré algebra which can be viewed as defining the quantum symmetries of the $ρ$-Minkowski space-time. The gauge theory model is left invariant under the action of the $ρ$-deformed Poincaré algebra. The kinetic part of the action is found to coincide with the one of the usual (commutative) electrodynamics.

hep-th↗

arXiv2024

Matter coupled to 3d Quantum Gravity: One-loop Unitarity

We expect quantum field theories for matter to acquire intricate corrections due to their coupling to quantum fluctuations of the gravitational field. This can be precisely worked out in 3d quantum gravity: after integrating out quantum gravity, matter fields are effectively described as noncommutative quantum field theories, with quantum-deformed Lorentz symmetries. An open question remains: Are such theories unitary or not? On the one hand, since these are effective field theories obtained after integrating out high energy degrees of freedom, we may expect the loss of unitarity. On the other hand, as rigorously defined field theories built with Lorentz symmetries and standing on their own, we naturally expect the conservation of unitarity. In an effort to settle this issue, we explicitly check unitarity for a scalar field at one-loop level in both Euclidean and Lorentzian space-time signatures. We find that unitarity requires adding an extra-term to the propagator of the noncommutative theory, corresponding to a massless mode and given by a representation with vanishing Plancherel measure, thus usually ignored in spinfoam path integrals for quantum gravity. This indicates that the inclusion of matter in spinfoam models, and more generally in quantum gravity, might be more subtle than previously thought.

hep-th↗

arXiv2023

Quantum causality in $κ$-Minkowski and related constraints

We study quantum causal structures in $1+1$ $κ$-Minkowski space-time described by a Lorentzian Spectral Triple whose Dirac operator is built from a natural set of twisted derivations of the $κ$-Poincaré algebra. We show that the Lorentzian Spectral Triple must be twisted to accommodate the twisted nature of the derivations. We exhibit various interesting classes of causal functions, including an analog of the light-cone coordinates. We show in particular that the existence of a causal propagation between two pure states, the quantum analogs of points, can exist provided quantum constraints, linking the momentum and the space coordinate, are satisfied. One of these constraints is a quantum analog of the speed of light limit.

math-ph↗