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Pierre Martin-Dussaud

Publications and source records attributed to Pierre Martin-Dussaud.

16 recordsLinked to original sources
arXiv2026

A Primer of Group Theory for Loop Quantum Gravity and Spin-foams

Calculations in Loop Quantum Gravity (LQG) and spin-foam theory rely heavily on the group theory of SU(2) and SL(2,C). Even though many monographs are devoted to this material, the various tools required (representation theory, harmonic analysis, recoupling theory, ...) are often scattered across different books, each with its own conventions and notations. This was the initial motivation for the present document, which serves three main purposes: a concise introduction for students to the essential mathematical tools of LQG, a convenient compendium of formulae for researchers, and a translation hub between the conventions of the main references. These notes are aimed both at physicists, who want their tools to be mathematically well-grounded, and at mathematicians, curious to see how some of their familiar abstract structures reveal the beauty of quantum gravity.

math-ph↗
arXiv2026

Causal structure in spin-foams

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin-foam models for quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin-foam model and discuss the role of the causal structure in the reconstruction of a semiclassical spacetime geometry.

gr-qc↗
arXiv2025

The lifetime of white hole remnants is $M^5$

The black-to-white hole scenario is a well-motivated proposal from non-perturbative quantum gravity concerning the final stage of black hole evaporation. In this framework, a black hole of initial mass $M$ undergoes Hawking evaporation over a timescale of order $M^3$ before tunneling into a long-lived white hole. Previous estimates suggest that the lifetime of the resulting white hole scales as $M^4$. In this short note, I argue that such estimates neglect key aspects of the white hole's internal dynamics, and I demonstrate that a more consistent timescale for the white hole lifetime is of order $M^5$.

gr-qc↗
arXiv2022

Spin-networks in the ZX-calculus

The ZX-calculus, and the variant we consider in this paper (ZXH-calculus), are formal diagrammatic languages for qubit quantum computing. We show that it can also be used to describe SU(2) representation theory. To achieve this, we first recall the definition of Yutsis diagrams, a standard graphical calculus used in quantum chemistry and quantum gravity, which captures the main features of SU(2) representation theory. Second, we show precisely how it embed within Penrose's binor calculus. Third, we subsume both calculus into ZXH-diagrams. In the process we show how the SU(2) invariance of Wigner symbols is trivially provable in the ZXH-calculus. Additionally, we show how we can explicitly diagrammatically calculate 3jm, 4jm and 6j symbols. It has long been thought that quantum gravity should be closely aligned to quantum information theory. In this paper, we present a way in which this connection can be made exact, by writing the spin-networks of loop quantum gravity (LQG) in the ZX-diagrammatic language of quantum computation.

quant-ph↗
arXiv2022

Fact-nets: towards a mathematical framework for relational quantum mechanics

The relational interpretation of quantum mechanics (RQM) has received a growing interest since its first formulation in 1996. Usually presented as an interpretational layer over the usual quantum mechanics formalism, it appears as a philosophical perspective without proper mathematical counterparts. This state of affairs has direct consequences on the scientific debate on RQM which still suffers from misunderstandings and imprecise statements. In an attempt to clarify those debates, the present paper proposes a radical reformulation of the mathematical framework of quantum mechanics which is relational from the start: fact-nets. The core idea is that all statements about the world, facts, are binary entities involving two systems that can be symmetrically thought of as observed and observer. We initiate a study of the fact-nets formalism and outline how it can shed new relational light on some familiar quantum features.

quant-ph↗
arXiv2022

An experiment to test the discreteness of time

Time at the Planck scale ($\sim 10^{-44}\,\mathrm{s}$) is an unexplored physical regime. It is widely believed that probing Planck time will remain for long an impossible task. Yet, we propose an experiment to test the discreteness of time at the Planck scale and estimate that it is not far removed from current technological capabilities.

gr-qc↗
arXiv2021

Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors

We study the semiclassical limit of a class of invariant tensors for infinite-dimensional unitary representations of $\mathrm{SL}(2,\mathbb{C})$ of the principal series, corresponding to generalized Clebsch-Gordan coefficients with $n\geq3$ legs. We find critical configurations of the quantum labels with a power-law decay of the invariants. They describe 3d polygons that can be deformed into one another via a Lorentz transformation. This is defined viewing the edge vectors of the polygons are the electric part of bivectors satisfying a (frame-dependent) relation between their electric and magnetic parts known as $γ$-simplicity in the loop quantum gravity literature. The frame depends on the SU(2) spin labelling the basis elements of the invariants. We compute a saddle point approximation using the critical points and provide a leading-order approximation of the invariants. The power-law is universal if the SU(2) spins have their lowest value, and $n$-dependent otherwise. As a side result, we provide a compact formula for $γ$-simplicity in arbitrary frames. The results have applications to the current EPRL model, but also to future research aiming at going beyond the use of fixed time gauge in spin foam models.

gr-qc↗
arXiv2021

The End of a Black Hole's Evaporation -- Part I

At the end of Hawking evaporation, the horizon of a black hole enters a physical region where quantum gravity cannot be neglected. The physics of this region has not been much explored. We characterise its physics and introduce a technique to study it.

gr-qc↗
arXiv2021

Searching for Coherent States: From Origins to Quantum Gravity

We discuss the notion of coherent states from three different perspectives: the seminal approach of Schroedinger, the experimental take of quantum optics, and the theoretical developments in quantum gravity. This comparative study tries to emphasise the connections between the approaches, and to offer a coherent short story of the field, so to speak. It may be useful for pedagogical purposes, as well as for specialists of quantum optics and quantum gravity willing to embed their perspective within a wider landscape.

quant-ph↗
arXiv2020

Relational structures of fundamental theories

General relativity and quantum mechanics have both revealed the relativity of certain notions that were previously thought to be absolute. I clarify the precise sense in which these theories are relational, and I argue that the various aspects of relationality pertain to the same movement in the progress of physical theories.

physics.hist-ph↗
arXiv2020

Black-to-White Hole Scenario: Foundation and Evaporation

A theory of quantum gravity is expected to change profoundly our understanding of black holes. Quantum theory has already shown, as a first approximation, that a black hole slowly evaporates. Non-perturbative quantum gravity also predicts that such an object could metamorphose into a white hole, its time-reverse. In this thesis, we study the foundations of such a scenario and propose a mathematical model that includes the phenomenon of evaporation.

gr-qc↗
arXiv2019

Evaporating black-to-white hole

We construct and discuss the form of the (effective) spacetime geometry inside a black hole undergoing a quantum transition to a white hole, taking into account the back-reaction of the component of the Hawking radiation falling into the hole.

gr-qc↗
arXiv2018

The notion of locality in relational quantum mechanics

The term 'locality' is used in different contexts with different meanings. There have been claims that relational quantum mechanics is local, but it is not clear then how it accounts for the effects that go under the usual name of quantum non-locality. The present article shows that the failure of 'locality' in the sense of Bell, once interpreted in the relational framework, reduces to the existence of a common cause in an indeterministic context. In particular, there is no need to appeal to a mysterious space-like influence to understand it.

quant-ph↗
arXiv2018

Interior metric and ray-tracing map in the firework black-to-white hole transition

The possibility that a black hole could tunnel into a white hole has recently received attention. Here we present a metric that improves the 'firework' metric: it describes the entire process and solves the Einstein equations everywhere except on a small transition surface that corresponds to the quantum tunnelling. We compute the corresponding ray-tracing map from past infinity to future infinity explicitly.

gr-qc↗