arXiv subjects

Jean-Pierre Gazeau

Publications and source records attributed to Jean-Pierre Gazeau.

At least 19 recordsLinked to original sources

arXiv2026

Earth as a Closed Life-Support System: Finite Buffers, Dynamical Thresholds, and Planetary Sustainability

Earth is nearly closed with respect to matter but open with respect to energy. We formulate planetary sustainability as a minimal nonequilibrium dynamical problem for coupled finite stocks and fluxes, using the operational language of closed ecological and engineered life-support systems: inventories, flux balances, recycling efficiencies, processing capacities, reserve times, and failure thresholds. The framework describes a competition between two finite buffers: resource stocks that can be depleted and waste-processing capacities that can be saturated. The physiological contrast between fasting and renal failure motivates a general reserve-time principle: the dominant constraint is the buffer that becomes critical first. Our nonlinear model couples a regenerative resource stock, an accumulated waste stock, and an aggregate activity variable. It exhibits a soft waste threshold, where accumulated waste suppresses growth while processing remains formally capable, and a hard threshold, where waste production exceeds maximal processing capacity. We extend the model to recycling and multiple resource and waste classes, give an explicit numerical example, and relate it to Spaceship Earth, planetary boundaries, Limits to Growth, and stock-pollution growth models. A multiscale analogy--cell, organism, planet--emphasizes that life-support functions combine degradation, recycling, transport, regulation, and removal. Carrying capacity thus emerges as a time-dependent property of coupled resource, waste, recycling, technological, and institutional dynamics: either resource depletion or elimination failure may become the binding constraint, depending on their characteristic reserve times.

physics.soc-ph↗

arXiv2026

Spectral-angular parametrization of open qudit dynamics: gap coordinates, Cartan structure, and GKLS decoupling

Every $n$-level density matrix can be diagonalized as $ρ=U\,\mathrm{diag}(p_1,\ldots,p_n)U^\dagger$, splitting it into an eigenvalue vector $(p_1,\ldots,p_n)$ and a unitary eigenbasis $U$. We introduce a new coordinate system on the eigenvalue vector alone: the \emph{gap coordinates} $r_a:=p_a-p_{a+1}\ge0$, $a=1,\ldots,n-1$. We show that $(r_1,\ldots,r_{n-1})$ are precisely the simple-root coordinates of the eigenvalue vector in the Cartan subalgebra of $A_{n-1}=\mathfrak{sl}(n)$, so that the spectral diagonal expands in the fundamental-coweight basis, $\mathsf D(\mathbf r)=\sum_a r_a\,ω_a^\vee$, and the $n-1$ eigenvalue-ordering inequalities collapse into the single linear constraint $\sum_a a\,r_a\le1$ defining a weighted simplex $R_{n-1}$. This identification yields closed-form expressions for the Fisher--Rao and Bures metrics at the maximally mixed state in terms of the inverse Cartan matrix of $A_{n-1}$, and for a piecewise-linear alternative to the standard definition of purity. On the angular side we give an explicit Tilma--Sudarshan-type coordinatization of the flag manifold $F_n\simeq\mathrm{SU}(n)/\mathbb T^{n-1}$ and a global coherent-state resolution of the identity on $F_n$, enabling an $\mathrm{SU}(n)$-covariant integral quantization of the flag variety. Under GKLS dynamics, the pair (gap coordinates, flag angles) exhibits a partial decoupling: the eigenvalue gaps evolve under dissipation alone, while the flag angles are driven by both the Hamiltonian and the dissipator, which we derive directly in these coordinates, including an explicit illustration on the real qutrit sector.

quant-ph↗

arXiv2026

The de Sitter Scalar Discrete Series: Gupta-Bleuler Structure and Holography

We show that scalar discrete-series unitary irreducible representations (UIRs) $Π_{p,0}$ ($p=1,2,\cdots$) of the de Sitter (dS) group $\mathrm{SO}_0(1,4)$ admit a dS-covariant Krein realization on the dS hyperboloid, endowed with a dS-invariant non-degenerate Klein-Gordon (KG) sesquilinear form, in which the group action is indecomposable and organizes naturally into a Gupta-Bleuler triplet. The positive- and negative-norm sectors are already present in the underlying Krein space, whereas a null sector emerges only at an intermediate stage, where the induced KG form becomes degenerate and its radical leads canonically to the physical quotient carrying the UIR $Π_{p,0}$. We further show that suitable limits of the bulk theory at the ``future'' and ``past'' conformal boundaries ${\mathcal{I}}^\pm$ give rise to dS-invariant boundary realizations endowed with induced kernel inner products. While the bulk negative-norm sector admits no independent boundary counterpart, the boundary realization retains the physical and gauge structures inherited from the bulk. The resulting boundary module nevertheless remains indecomposable, with its physical quotient carrying the discrete-series representation $Π_{p,0}$. The antipodal symmetry provides a natural relation between the realizations on ${\mathcal{I}}^+$ and ${\mathcal{I}}^-$, ensuring the consistency of the boundary construction and its geometric interpretation. At the heart of the analysis lies a Fourier-type bulk-boundary transform that provides a dS-covariant identification of the bulk and boundary physical sectors, establishing a one-to-one intertwining correspondence between the bulk and boundary realizations of $Π_{p,0}$ while preserving reflection positivity.

math-ph↗

arXiv2026

Quantum mechanics over real numbers fully reproduces standard quantum theory

Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome. However, a highly cited 2021 result claimed that any quantum theory based on real numbers is experimentally falsifiable via network Bell experiments. Yet, it remains an open question whether this falsification applies to all real-valued theories. Here we show that this conclusion rests on an incomplete real formulation, and we present a rigorous real-valued framework that perfectly reproduces all predictions of standard quantum mechanics. We demonstrate that the standard real tensor product ($\otimes_{\mathbb{R}}$) used in previous no-go theorems is algebraically incompatible with the rich structure of conventional quantum mechanics. We present a real framework based on Kähler space and prove that it is exactly isomorphic to established quantum mechanics via an explicit bijection $γ$. The isomorphism extends to composite systems through a symplectic composition rule $\otimes^{\ks}$ that replaces the Kronecker product. Consequently, our formulation achieves the maximal $\mathrm{CHSH}_{3}$ violation of $6\sqrt{2}$ using purely real variables, demonstrating that the no-go theorem is specific to a particular real representation of states and operators and to the composition rule $\otimes_\mathbb{R}$ built upon it, neither of which extends to the present Kähler framework. These results demonstrate that complex numbers are not fundamentally required by nature; rather, they encode a deeper real geometric structure that governs quantum interference and entanglement, settling this long debate.

quant-ph↗

arXiv2026

Infrared Spectral Gap in a Gluonic Dark Sector and the Galactic Acceleration Scale

We further develop a trace-anomaly-motivated gluonic scenario in which cold dark matter (CDM) is modeled as a long-lived color-singlet Bose-Einstein condensate seeded at the QCD confinement transition. Specifically, guided by the near-universality of the galactic acceleration scale $g^{}_\dagger \simeq (1\text{--}2)\times10^{-10}\,\mathrm{m\,s^{-2}}$ inferred from the RAR, we hypothesize that this relic gluonic condensate organizes, at galactic distances, into a spectrally rigid lowest-weight structure characterized by a protected infrared gap. Within an effective representation-theoretic framework, Lorentz covariance together with positive-energy lowest-weight unitarity naturally favors the AdS algebra $\mathfrak{so}(2,3)$ as the minimal algebraic structure supporting such a discrete tower of states. The resulting condensate produces, by construction, a cored halo profile with finite total mass $M_h$. Normalizing this profile by the observed approximate universality of the central DM surface density, $Σ_0\simeq141\,M_\odot\,\mathrm{pc}^{-2}$, yields a universal characteristic acceleration $g^{}_\star ={G\, M_h}/{r_{\rm c}^2} \simeq π^2 G\,Σ_0 \simeq 1.9\times10^{-10}\,\mathrm{m\,s^{-2}}$, independent of the particular halo scale; since $Σ_0$ fixes the final expression, the dependence on the collective correlation length $r_{\rm c}$ drops out. Notably, its predicted value lies well within the empirical range of the acceleration scale inferred from the RAR. We also provide an illustrative comparison with representative rotation curves from the SPARC database, indicating phenomenological compatibility of the finite-mass profile with realistic baryonic decompositions. This comparison is not a precision fit to the full SPARC sample, and the agreement with the RAR scale should not be interpreted as a first-principles derivation of the RAR itself.

hep-th↗

arXiv2026

Finite-resolution measurement induces topological curvature defects in spacetime

We show that regularizing $(2+1)$-dimensional Minkowski spacetime with a finite-resolution Gaussian probe, analogous to Weyl-Heisenberg (Gabor) signal analysis and related quantization, induces a curved geometry with a topological defect. The regularized metric replaces $r^2$ by $r^2+σ^2$ in the angular part, where $σ$ is the resolution scale from the width of the Gaussian probe. The resulting Gaussian curvature integrates to $-2π$, independently of $σ$. This curvature defines an effective stress-energy source with universal total energy $E_{\text{eff}}=-1/(4G)$. The limit $σ\to0$ leads to distributional Dirac-delta curvature and to appearance of topological defect at the origin. These results show that finite spatial resolution measurement does not merely smooth singularities but can shape spacetime geometry.

gr-qc↗

arXiv2026

Massless Representations in Conformal Space and Their de Sitter Restrictions

The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2), combining rigorous representation-theoretic analysis with fully explicit constructions. It systematically develops these representations, including the derivation of invariant bilinear forms and Casimir operators, and constructs vertex operators and two-point functions for low-helicity fields. A central and distinctive contribution is the introduction of a canonical Clifford-split-octonion framework, in which 8-component Majorana spinors are realized within an alternative composition algebra, providing a unified and intrinsically defined setting for the algebraic, spinorial, and geometric structures underlying the theory. By bridging abstract symmetry principles with concrete computational methods and physically motivated applications in quantum field theory and cosmology, the monograph advances both conceptual clarity and technical control. While primarily addressed to researchers in mathematical physics and related fields, the exposition is carefully structured to guide advanced graduate students through subtle constructions, maintaining accessibility without compromising mathematical precision.

math-ph↗

arXiv2026

A Mnemonic Matrix Rule for (Split) Octonionic Multiplication and its Extension to the Cayley--Dickson Tower

We present a compact mnemonic device for computing the product of two (split) octonions written in Cayley--Dickson form q+l p with q,p in H. The rule appears as a simple (R+L) pattern of right-ordered and left-ordered (quaternionic) products inside a 2X2 quaternionic matrix model. The pattern extends verbatim to all algebras in the Cayley--Dickson tower, providing an efficient computational tool in non-associative settings. To our knowledge, this explicit ``(R+L)'' mnemonic does not appear in the classical literature on octonions or composition algebras.

math.RA↗

arXiv2025

The Geometry of Qubit Decoherence: Linear vs. Nonlinear Dynamics in the Bloch Ball

We present two complementary approaches to the GKSL equation for an open qubit. The first, based on linearity, yields solutions illustrated by mixed states trajectories in the Bloch ball, including non-random asymptotic fixed points, and exceptional points. The second, exploiting the SU(2) symmetry, leads to a nonlinear dynamical system that separates angular dynamics from radial dissipation. This symmetry-based perspective offers a promising route toward generalisation to open qudits.

quant-ph↗

arXiv2025

A purely geometrical Aharonov-Bohm effect

We present an application of the affine covariant integral quantization (ACIQ) (Adv. Oper. Theory, 5, 2020; Adv. Oper. Theory, 7, 2022) to quantum mechanics on the punctured plane. The associated four-dimensional phase space is identified with the similitude group SIM(2), which comprises translations, rotations, and dilations of the plane. Due to the topology of the punctured plane, our quantization procedure gives rise to an affine vector potential. This potential can be interpreted as the Aharonov-Bohm (AB) gauge field produced by an infinite solenoid. This observation supports a reinterpretation of the AB effect: it emerges from the topological constraint imposed by the impenetrable coil rather than from an externally applied classical gauge field. In addition to this gauge structure, ACIQ also generates a repulsive, centrifugal-like scalar potential, a feature already encountered when applying ACIQ to motion on the half-line, whose phase space is the open half-plane. These results provide a new perspective on the AB effect, highlighting the central roles of topology and symmetry in quantum mechanics.

quant-ph↗

arXiv2025

A unified framework for graviton, "partially massless" graviton, and photon fields in de Sitter spacetime under conformal symmetry

We develop a conformally invariant (CI) framework in $(1+3)$-dimensional de Sitter (dS) spacetime, that unifies the descriptions of graviton, ``partially massless'' graviton, and photon fields. This framework is grounded in a rigorous group-theoretical analysis in the Wigner sense and employs Dirac's six-cone formalism. Originally introduced by Dirac, the concept of conformal space and the six-cone formalism were used to derive the field equations for spinor and vector fields in $(1+3)$-dimensional Minkowski spacetime in a manifestly CI form. Our framework extends this approach to dS spacetime, unifying the treatment of massless and ``partially massless'' fields with integer spin $s>0$ under conformal symmetry. This unification enhances the understanding of fundamental aspects of gravitational theories in curved backgrounds.

gr-qc↗

arXiv2025

Holomorphic Discrete Series of SU(1,1): Orthogonality Relations, Character Formulas, and Multiplicities in Tensor Product Decompositions

The SU$(1,1)$ group plays a fundamental role in various areas of physics, including quantum mechanics, quantum optics, and representation theory. In this work we revisit the holomorphic discrete series representations of SU$(1,1)$, with a focus on orthogonality relations for matrix elements, character formulas of unitary irreducible representations (UIRs), and the decomposition of tensor products of these UIRs. Special attention is given to the structure of these decompositions and the associated multiplicities, which are essential for understanding composite systems and interactions within SU$(1,1)$ symmetry frameworks. These findings offer deeper insights into the mathematical foundations of SU$(1,1)$ representations and their significance in theoretical physics.

math.GR↗

arXiv2025

A misleading naming convention: de Sitter `tachyonic' scalar fields

We revisit the concept of de Sitter (dS) 'tachyonic' scalar fields, characterized by discrete negative squared mass values, and assess their physical significance through a rigorous Wigner-inspired group-theoretical analysis. This perspective demonstrates that such fields, often misinterpreted as inherently unstable due to their mass parameter, are best understood within the framework of unitary irreducible representations (UIRs) of the dS group. The discrete mass spectrum arises naturally in this representation framework, offering profound insights into the interplay between dS relativity and quantum field theory. Contrary to their misleading nomenclature, we argue that the 'mass' parameter associated with these fields lacks intrinsic physical relevance, challenging traditional assumptions that link it to physical instability. Instead, any perceived instability originates from mismanagement of the system's inherent gauge invariance rather than the fields themselves. A proper treatment of this gauge symmetry, particularly through the Gupta-Bleuler formalism, restores the expected characteristics of these fields as free quantum entities in a highly symmetric spacetime. This study seeks to dispel misconceptions surrounding dS 'tachyonic' fields, underscoring the importance of precise terminology and robust theoretical tools in addressing their unique properties.

gr-qc↗

arXiv2024

Universality of the Weyl-Heisenberg symmetry and its covariant quantisations

The Weyl-Heisenberg symmetries originate from translation invariances of various manifolds viewed as phase spaces, e.g. Euclidean plane, semi-discrete cylinder, torus, in the two-dimensional case, and higher-dimensional generalisations. In this review we describe, on an elementary level, how this symmetry emerges through displacement operators and standard Fourier analysis, and how their unitary representations are used both in Signal Analysis (time-frequency techniques, Gabor transform) and in quantum formalism (covariant integral quantizations and semi-classical portraits). An example of application of the formalism to the Majorana stellar constellation in the plane is presented.

quant-ph↗

arXiv2024

Matter-antimatter (a)symmetry in de Sitter Universe

We investigate the matter-antimatter properties of elementary systems, modeled as free quantum fields, within the global structure of de Sitter spacetime. By leveraging the distinctive causal and analytic properties of de Sitter spacetime, we propose that matter-antimatter asymmetry could emerge as an observer-dependent effect shaped by time orientation within a local causal patch, rather than as a fundamental property of de Sitter Universe itself. This kinematic perspective complements, rather than replaces, standard dynamical processes (such as baryon number violation, $\texttt{CP}$ violation, and nonequilibrium processes) that fulfill Sakharov's criteria. Within this framework, the limited presence of antimatter in our predominantly matter-filled Universe, specifically within the causal patch of de Sitter spacetime under consideration, may arise from these mechanisms, though through pathways distinct from conventional interpretations.

gr-qc↗

arXiv2024

Matrix Elements and Characters of the Discrete Series ("Massive") Unitary Irreducible Representations of Sp(4,R)

This paper obtains the matrix elements and characters of the discrete series unitary irreducible representations (UIRs) of the Sp$(4,\mathbb{R})$ group. With an isomorphic relationship to the two-fold covering of SO$_0(2,3)$ (Sp$(4,\mathbb{R}) \sim$ SO$_0(2,3)\times \mathbb{Z}_2$), this group holds particular importance as the kinematical/relativity group within the framework of ($1+3$-dimensional) anti-de Sitter spacetime.

math-ph↗

arXiv2024

Anti-de Sitterian "massive" elementary systems and their Minkowskian and Newton-Hooke contraction limits

We elaborate the definition and properties of "massive" elementary systems in the $(1+3)$-dimensional Anti-de Sitter (AdS$_4$) spacetime, on both classical and quantum levels. We fully exploit the symmetry group {isomorphic to} Sp$(4,R)$, that is, the two-fold covering of SO$_0(2,3)$ (Sp$(4,\mathbb R) \sim$ SO$_0(2,3)\times \mathbb Z_2$), recognized as the relativity/kinematical group of motions in AdS$_4$ spacetime. In particular, we discuss that the group coset Sp$(4,\mathbb R)/\mathrm{S}\big(\mathrm{U}(1)\times \mathrm{SU}(2)\big)$, as one of the Cartan classical domains, can be interpreted as a phase space for the set of free motions of a test massive particle on AdS$_4$ spacetime; technically, in order to facilitate the computations, the whole process is carried out in terms of complex quaternions. The (projective) unitary irreducible representations (UIRs) of the Sp$(4,R)$ group, describing the quantum version of such motions, are found in the discrete series of the Sp$(4,\mathbb R)$ UIRs. We also describe the null-curvature (Poincaré) and non-relativistic (Newton-Hooke) contraction limits of such systems, on both classical and quantum levels. On this basis, we unveil the dual nature of "massive" elementary systems living in AdS$_4$ spacetime, as each being a combination of a Minkowskian-like elementary system {with positive proper mass}, with an isotropic harmonic oscillator arising from the AdS$_4$ curvature and viewed as a Newton-Hooke elementary system. This matter-vibration duality will take its whole importance in the quantum regime (in the context of the validity of the equipartition theorem) in view of its possible rôle in the explanation of the current existence of dark matter.

math-ph↗

arXiv2024

Regularized quantum motion in a bounded set: Hilbertian aspects

It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous set of self-adjoint extensions. We prove that essential self-adjointness can be recovered by symmetrically weighting the momentum operator with a positive bounded function approximating the indicator function of the considered interval. This weighted momentum operator is consistently obtained from a similarly weighted classical momentum through the so-called Weyl-Heisenberg covariant integral quantization of functions or distributions.

math-ph↗