arXiv subjects

Norma G. Sanchez

Publications and source records attributed to Norma G. Sanchez.

At least 19 recordsLinked to original sources

arXiv2025

Entanglement and Minimal Hilbert Space in the Classical Dual States of Quantum Theory

A precise physical description and understanding of the classical dual content of quantum theory is necessary in many disciplines today: from concepts and interpretation to quantum technologies and computation. In this paper we investigate Quantum Entanglement with the new approach APL Quantum 2, 016104 (2025) on dual Classicalization. Thus, the results of this paper are twofold: Entanglement and Classicalization and the relationship between them. Classicalization truly occurs only under the action of the Metaplectic group Mp(n) (Minimal Representation group, double covering of the Symplectic group). Some of the results of this paper involves the computation and analysis of the entanglement for different types of coherent (coset and non coset) states and topologies: in the circle and the cylinder. We project the entangled wave functions onto the even (+) and odd (-) irreducible Hilbert Mp(n) subspaces, and compute their square norms: Entanglement Probabilities P++, P--, P+-, (eg in the same or in the different subspaces), and the Total sum of them, and more. These theoretical and conceptual results can be of experimental and practical real-world interest.

quant-ph↗

arXiv2025

Classical (ontological) dual states in quantum theory and the minimal group representation Hilbert space

We investigate the classical aspects of Quantum theory and under which description Quantum theory does appear Classical. Although such descriptions or variables are known as "ontological" or "hidden", they are not hidden at all, but are dual classical states (in the sense of the general classical-quantum duality of Nature). The application of the Minimal Group Representation immediately classicalizes the system, Mp(2) emerging as the group of the classical-quantum duality symmetry. (Abridged)

quant-ph↗

arXiv2024

Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity

A new formalism is introduced describe the physical and geometric content of quantum spacetime. It is based in the Minimum Group Representation Principle. New results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space-times. Our main results here are: (i) The Berry phases for inflation, for the cosmological perturbations, and its expression in terms of observables, as the spectral scalar and tensor indices, $n_S$ an $n_T$, and their ratio $r$. The Berry phase for de Sitter inflation is imaginary, its sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) $Mp(n)$ representation for quantum de Sitter space-time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp(n)$ group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) The mean $Mp(2)$ generator values are related to the space-time topological charge. (v) The basic even and odd $n$ -sectors of the Hilbert space are intrinsic to the quantum spacetime and its discrete levels (continuum for $n \rightarrow \infty$) and are it entangled. (vi) The gravity or cosmological domains on one side and another of the Planck scale are entangled. Examples: The primordial quantum trans-Planckian de Sitter vacuum and the late classical gravity de Sitter vacuum today; the central quantum reqion and the external classical region of black holes. The classical and quantum dual gravity regions of the space-time are entangled. (vii) The general classical-quantum gravity duality is associated to the Metaplectic $Mp(n)$ group symmetry which provides the complete full covering of the phase space and of the quantum space-time mapped from it.

physics.gen-ph↗

arXiv2024

Quantum Trans-Planckian Physics inside Black Holes and its Spectrum

We provide a quantum unifying picture for black holes of all masses and their main properties covering classical, semiclassical, Planckian and trans-Planckian gravity domains: Space-time, size, mass, vacuum ("zero point") energy, temperature, partition function, density of states and entropy. Novel results of this paper are: Black hole {\bf interiors} are always {\bf quantum}, trans-Planckian and of constant curvature: This is so for {\it all} black holes, including the most macroscopic and astrophysical ones. The black hole interior trans-Planckian vacuum is similar to the earliest cosmological vacuum which classical gravity dual is the low energy gravity vaccum: today dark energy. There is {\it no} singularity boundary at $r = 0$, not at any other place: The quantum space-time is {\bf totally regular}. The {\it quantum} Penrose diagram of the Schwarschild-Kruskal black hole is displayed. The complete black hole {\it instanton} (imaginary time) covers the known classical Gibbons-Hawking instanton plus a {\it new} central highly dense {\it quantum core} of Planck length radius and {\it constant curvature}. The complete partition function, entropy, temperature, decay rate, discrete levels and density of states {\it all} include the trans-Planckian domaine. The semiclassical black hole entropy (the Bekenstein-Hawking entropy)$ (\sqrt{n})^2$ "interpolates" between the quantum point particle (QFT) entropy $(n)$ and the quantum string entropy $\sqrt{n}$, while the quantum trans-Planckian entropy is $1/(\sqrt{n})^2$. Black hole evaporation ends as {\it a pure (non mixed)} quantum state of particles, gravitons and radiation.

hep-th↗

arXiv2024

Quantum Space-Time Symmetries: A Principle of Minimum Group Representation

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of {\it quantum space-time}: This is the principle of {\it minimal group representation} that allows to consistently and simultaneously obtain a natural description of the spacetime dynamics and the physical states admissible in it. The theoretical construction is based on the physical states, average values of the Metaplectic group $Mp(n)$ generators: the double covering of $SL(2C)$ in a vector representation, with respect to the {\it coherent states} carrying the spin weight. Our main results here are: (i) A connection between the Metaplectic symmetry generators and the physical state dynamics. (ii) The ground states are coherent states, of Perelomov-Klauder type of the Metaplectic group dividing the Hilbert space into {\it even} and {\it odd} states. (iii) The physical states have spin contents $s = 0,\; 1/2, \;1,\; 3/2$ and $2$. (iv) The generators introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) A coherent physical state of spin 2 is obtained naturally related to the metric tensor. (vi) This is {\it naturally discretized} by the discrete series in the $n$ number representation, reaching the classical (continuous) space-time for $n$ $\rightarrow\infty$. (vii) A relation emerges between the coherent state metric eigenvalue $α$ and the black hole entropy through the Planck length. The lowest level of the quantum space-time spectrum, $n = 0$ and its characteristic length, yields a minimum entropy for the black hole history.

physics.gen-ph↗

arXiv2023

Coherent states of quantum spacetimes for black holes and de Sitter spacetime

We provide a group theory approach to coherent states describing quantum space-time and its properties. This provides a relativistic framework for the metric of a Riemmanian space with bosonic and fermionic coordinates, its continuum and discrete states, and a kind of {\it"quantum optics"} for the space-time. {\bf New} results of this paper are: (i) The space-time is described as a physical coherent state of the complete covering of the SL(2C) group, eg the Metaplectic group Mp(n). (ii) (The discrete structure arises from its two irreducible: $\textit{even}$ $(2n)$ and $\textit{odd}$ $(2n\;+\;1)\;$ representations, ($n = 1,\, 2, \,3\,...$ ), spanning the complete Hilbert space $\mathcal{H} = \mathcal{H}_{odd}\oplus \mathcal{H}_{even}$. Such a global or {\it complete} covering guarantees the CPT symmetry and unitarity. Large $n$ yields the classical and continuum manifold, as it must be. (iii) The coherent and squeezed states and Wigner functions of quantum-space-time for black holes and de Sitter, and (iv) for the quantum space-imaginary time (instantons), black holes in particular. They encompass the semiclassical space-time behaviour plus high quantum phase oscillations, and notably account for the classical-quantum gravity duality and trans-Planckian domain. The Planck scale consistently corresponds to the coherent state eigenvalue $α= 0$ (and to the $n = 0$ level in the discrete representation). It is remarkable the power of coherent states in describing both continuum and discrete space-time. The quantum space-time description is {\it regular}, there is no any space-time singularity here, as it must be.

gr-qc↗

arXiv2023

Dark Energy is the Cosmological Quantum Vacuum Energy of Light Particles-The Axion and the Lightest Neutrino

We uncover the general mechanism producing the dark energy(DE). This is only based on well known quantum physics and cosmology. We show that the observed DE originates from the cosmological quantum vacuum of light particles which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as log a(t) where a(t) is the scale factor, while the particle contributions dilute as 1/a^3(t), as it must be for massive particles. The DE equation of state P = w(z)H turns to be w(z)<-1 with w(z) asymptotically reaching the value -1 from below.A scalar particle can produce the observed DE through its quantum cosmological vacuum provided:(i)its mass is of the order of 10^{-3} eV = 1 meV,(ii) it is very weakly coupled and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the DE. We find that w(z=0) is slightly below -1 by an amount ranging from [-1.5 10^{-3}] to [-8 10^{-3}] and we predict the axion mass to be in the range between 4 and 5 meV. We find that the universe will expand in the future faster than the de Sitter universe, as an exponential in the square of the cosmic time. DE arises from the quantum vacua of light particles in FRW cosmological space time in an analogous way to the Casimir effect in Minkowski spacetime with non trivial boundaries.

astro-ph↗

arXiv2022

Galaxy Phase-Space Density Data Preclude that Bose-Einstein Condensate be the Total Dark Matter

Light scalars (as the axion) with mass m ~ 10^{-22} eV forming a Bose-Einstein condensate (BEC) exhibit a Jeans length in the kpc scale and were therefore proposed as dark matter (DM) candidates. Our treatment here is generic, independent of the particle physics model and applies to all DM BEC, in or out of equilibrium. Two observed quantities crucially constrain DM in an inescapable way: the average DM density rho_{DM} and the phase-space density Q. The observed values of rho_{DM} and Q in galaxies today constrain both the possibility to form a BEC and the DM mass m. These two constraints robustly exclude axion DM that decouples just after the QCD phase transition. Moreover, the value m ~ 10^{-22} eV can only be obtained with a number of ultrarelativistic degrees of freedom at decoupling in the trillions which is impossible for decoupling in the radiation dominated era. In addition, we find for the axion vacuum misalignment scenario that axions are produced strongly out of thermal equilibrium and that the axion mass in such scenario turns to be 17 orders of magnitude too large to reproduce the observed galactic structures. Moreover, we also consider inhomogenous gravitationally bounded BEC's supported by the bosonic quantum pressure independently of any particular particle physics scenario. For a typical size R ~ kpc and compact object masses M ~ 10^7 Msun they remarkably lead to the same particle mass m ~ 10^{-22} eV as the BEC free-streaming length. However, the phase-space density for the gravitationally bounded BEC's turns to be more than sixty orders of magnitude smaller than the galaxy observed values. We conclude that the BEC's and the axion cannot be the DM particle. However, an axion in the mili-eV scale may be a relevant source of dark energy through the zero point cosmological quantum fluctuations.

astro-ph.CO↗

arXiv2022

Warm Dark Matter Galaxies with Central Supermassive Black-Holes

We generalize the Thomas-Fermi approach to galaxy structure to include self-consistently and non-linearly central supermassive black holes. This approach naturally incorporates the quantum pressure of the warm dark matter (WDM) particles and shows its full powerful and clearness in the presence of supermassive black holes (SPMHs). We find the main galaxy and central black hole magnitudes: halo radius r_h , halo mass M_h, black hole mass M_BH, velocity dispersion, phase space density, with their realistic astrophysical values, masses and sizes over a wide galaxy range. The SMBH masses arise naturally in this framework. Our extensive numerical calculations and detailed analytic resolution show that with SMBH's, both WDM regimes: classical (Boltzmann dilute) and quantum (compact) do necessarily co-exist in any galaxy: from the smaller and compact galaxies to the largest ones. The transition from the quantum to the classical region occurs precisely at the same point r_A where the chemical potential vanishes. A novel halo structure with three regions shows up: A small quantum compact core of radius r_A around the SMBH, followed by a less compact region till the BH influence radius r_i, and then for r> r_i the known halo galaxy shows up with its astrophysical size. Three representative families of galaxy plus central SMBH solutions are found and analyzed:small, medium and large galaxies having SMBH masses of 10^5, 10^7 and 10^9 M_sun respectively. A minimum galaxy size and mass ~ 10^7 M_sun larger than the one without SMBH is found. Small galaxies in the range 10^4 M_sun < M_h < 10^7 M_sun cannot harbor central SMBHs. We find novel scaling M_BH - r_h - M_h relations. The galaxy equation of state is derived: The pressure P(r) takes huge values in the SMBH vecinity and then sharply decreases entering the classical region following a local perfect gas behaviour.(Abridged)

astro-ph.GA↗

arXiv2022

Quantum Discrete Levels of the Universe from the Early Trans-Planckian Vacuum to the Late Dark Energy

The standard model of the universe is further completed back in time before inflation in agreement with observations, classical-quantum gravity duality and quantum space-time. Quantum vacuum energy bends the space-time and produces a constant curvature de Sitter background. We link de Sitter universe and the cosmological constant to the (classical and quantum) harmonic oscillator. Quantum discrete cosmological levels are found: size, time, vacuum energy, Hubble constant and gravitational (Gibbons-Hawking) entropy from the very early trans-planckian vacuum to the classical today vacuum energy. For each level $n = 0, 1, 2,...$, the two: post and pre (trans)-planckian phases are covered: In the post-planckian universe, the levels (in planck units) are: Hubble constant $H_{n} = {1}/\sqrt{(2n + 1)}$, vacuum energy $Λ_{n} = 1/(2n + 1)$, entropy $S_n = (2n + 1)$. As $n$ increases, radius, mass and $S_n$ increase, $H_n$ and $Λ_n$ decrease and {\it consistently} the universe {\it classicalizes}. In the pre-planckian (trans-planckian) phase, the quantum levels are: $H_{Qn} = \sqrt{(2n + 1)},\; Λ_{Qn} = (2n + 1)/1,\; S_{Qn} = 1/(2n + 1)$, $Q$ denoting quantum. The $n$-levels cover {\it all} scales from the far past highest excited trans-planckian level $n = 10^{122}$ with finite curvature, $Λ_Q = 10^{122}$ and minimum entropy $S_Q = 10^{-122}$, $n$ decreases till the planck level $(n = 0)$ and enters the post-planckian phase e.g: $n = 1, 2,...,n_{inflation} = 10^{12},... ,n_{cmb} = 10^{114},...,n_{reoin} = 10^{118},...,n_{today} = 10^{122}$ with the most classical value $H_{today} = 10^{-61}$, $Λ_{today} = 10^{-122}$, $S_{today} = 10^{122}$. We implement the Snyder-Yang algebra in this context yielding a consistent group-theory realization of quantum discrete de Sitter space-time, classical-quantum gravity duality symmetry and a clarifying unifying picture.(Abridged)

physics.gen-ph↗

arXiv2021

Gravitation And the Universe from large Scale-Structures: The GAUSS mission concept

Today, thanks in particular to the results of the ESA Planck mission, the concordance cosmological model appears to be the most robust to describe the evolution and content of the Universe from its early to late times. It summarizes the evolution of matter, made mainly of dark matter, from the primordial fluctuations generated by inflation around $10^{-30}$ second after the Big-Bang to galaxies and clusters of galaxies, 13.8 billion years later, and the evolution of the expansion of space, with a relative slowdown in the matter-dominated era and, since a few billion years, an acceleration powered by dark energy. But we are far from knowing the pillars of this model which are inflation, dark matter and dark energy. Comprehending these fundamental questions requires a detailed mapping of our observable Universe over the whole of cosmic time. The relic radiation provides the starting point and galaxies draw the cosmic web. JAXA's LiteBIRD mission will map the beginning of our Universe with a crucial test for inflation (its primordial gravity waves), and the ESA Euclid mission will map the most recent half part, crucial for dark energy. The mission concept, described in this White Paper, GAUSS, aims at being a mission to fully map the cosmic web up to the reionization era, linking early and late evolution, to tackle and disentangle the crucial degeneracies persisting after the Euclid era between dark matter and inflation properties, dark energy, structure growth and gravitation at large scale.

astro-ph.CO↗

arXiv2020

Predictive Physics of Inflation and Grand Unification for and from the CMB observations

This White Paper for the CNRS IN2P3 Prospective 2020 focuses on realistic and timely situations of inflation in connection with the CMB, gravitational and particle physics, adding inter-disciplinarity and unification values within a strongly predictive physical approach. The formulation of inflation in the Ginsburg-Landau approach developed by de Vega and Sanchez [1] and by Boyanovsky, de Vega, Sanchez and Destri [2]-[4] clarifies and places inflation in the setting of the effective field theories of particle physics. In addition, it sets up a clean way to directly confront the inflationary predictions with the available and forthcoming CMB data and select a definitive model. All CMB + LSS data until now show how powerful is the Ginsburg-Landau effective theory of inflation in predicting observables in agreement with observations including the inflation energy scale and the inflaton potential, and which has much more to provide in the future. It paves the way to discoveries, new learning and understanding.

gr-qc↗

arXiv2019

New Quantum Phase of the Universe before Inflation and its Cosmological and Dark Energy Implications

The physical history of the Universe is completed by including the quantum planckian and trans-planckian phase before Inflation in the Standard Model of the Universe in agreement with observations. A new quantum precursor phase appears beyond the Planck scale. We extend de Sitter universe to the quantum domain: classical-quantum de Sitter duality. As a result: The classical and quantum dual de Sitter Temperatures and Entropies are naturally included, and the different (classical, semiclassical, quantum planckian and super-planckian) de Sitter regimes characterized in a precise and unifying way. Relevant cosmological examples as Inflation and Dark Energy are described. This allows to find in a simple and consistent way: Quantum Inflationary spectra and their CMB observables, including in particular the classical known Inflation spectra and the quantum corrections to them. A unifying picture for the Universe epochs and their quantum precursors emerges with the cosmological constant as the vacuum energy, entropy and temperature of the Universe, shedding light into the cosmological constant problem (Abridged).

gr-qc↗

arXiv2019

New Quantum Structure of the Space-Time

We start from quantum theory (instead of general relativity) to approach quantum gravity within a minimal setting and promote the space-time coordinates to quantum non-commuting operators. Comparison to the harmonic oscillator global phase space is enlighting. The phase space instanton (X, P = iT) describes the hyperbolic quantum space-time structure and generates the quantum light cone. The classical Minkowski space-time null generators X = T dissapear at the quantum level replaced by four Planck scale hyperbolae and a new quantum Planck scale vacuum region emerges. We describe the quantum Rindler and quantum Schwarzshild-Kruskal space-time structures. The horizons and the r=0 singularity are quantum mechanically erased. The four Kruskal regions merge inside a single quantum Planck scale "world". The quantum space-time structure consists of hyperbolic discrete levels of odd numbers (2n + 1) (in Planck units ), n = 0, 1, 2.... . The mass levels are the square root of (2n + 1). Large n are semiclassical tending towards a classical continuum space-time. Low n are quantum, the lowest mode (n = 0) being the Planck scale. Two dual branches are present covering the whole mass spectrum: from the largest astrophysical objects to the quantum elementary particles passing by the Planck mass. Black holes belong to both branches. (Abridged)

physics.gen-ph↗

arXiv2019

Constraining Dark Matter models with extremely distant galaxies

The investigation of distant galaxy formation and evolution is a powerful tool to constrain dark matter scenarios, supporting and in some cases surpassing other astrophysical and experimental probes. The recent completion of the Hubble Frontier Fields (HFF) programme combining ultra-deep Hubble Space Telescope observations and the magnification power of gravitational lensing produced by foreground galaxy clusters has enabled the detection of the faintest primordial galaxies ever studied. Here we show how the number density of such primordial galaxies allows to constrain a variety of DM models alternative to CDM. In particular, it provides stringent limits on the mass of thermal WDM candidates, on the parameter space of sterile neutrino production models, and on other DM scenarios featuring particles in the keV mass range which is also supported by recent detections of a 3.5keV X-ray line. These constraints are robust and independent of the baryonic physics modeling of galaxy formation and evolution. Fuzzy DM (ultralight DM particles) results strongly disfavored.

astro-ph.CO↗

arXiv2018

The Classical-Quantum Duality of Nature. New Variables for Quantum Gravity

The classical-quantum duality at the basis of quantum theory is here extended to the Planck scale domain. The classical/semiclassical gravity (G) domain is dual (in the precise sense of the classical-quantum duality) to the quantum (Q) elementary particle domain through the Planck scale. This duality is universal. From the gravity and quantum variables (G, Q), we define new (QG) quantum gravity variables QG = (1/2) (G + Q) which include all (classical, semiclassical and quantum gravity) domains and the elementary particle domain passing by the Planck scale. Two values of G or Q variables are necessary for each variable QG. The complete analytic extension of the QG variables is performed. This allows us to reveal the classical-quantum duality of the Schwarzschild-Kruskal space-time: The exterior regions are classical/semiclassical while the interior is totally quantum, its boundaries being the Planck scale. Exterior and interior lose their difference near the horizon which turns to be quantum dressed, " l'horizon habille' ". QG variables are naturally invariant under G --> Q and conversely. Space-time reflections, antipodal symmetry and PT or CPT symmetry are contained in the QG symmetry, which also shed insight into the global properties of the Kruskal manifold and its present renewed interest...(Abridged)

physics.gen-ph↗

arXiv2017

Fundamental physics with the Hubble Frontier Fields: constraining Dark Matter models with the abundance of extremely faint and distant galaxies

We show that the measured abundance of ultra-faint lensed galaxies at $z\approx 6$ in the Hubble Frontier Fields (HFF) provides stringent constraints on the parameter space of i) Dark Matter models based on keV sterile neutrinos; ii) the "fuzzy" wavelike Dark Matter models, based on Bose-Einstein condensate of ultra-light particles. For the case of the sterile neutrinos, we consider two production mechanisms: resonant production through the mixing with active neutrinos and the decay of scalar particles. For the former model, we derive constraints for the combination of sterile neutrino mass $m_ν$ and mixing parameter $\sin^2(2θ)$ which provide the tightest lower bounds on the mixing angle (and hence on the lepton asymmetry) derived so far by methods independent of baryonic physics. For the latter we compute the allowed combinations of the scalar mass, its coupling to the Higgs field, and the Yukawa coupling of the scalar to the sterile neutrinos. We compare our results to independent, existing astrophysical bounds on sterile neutrinos in the same mass range. For the case of "fuzzy" Dark Matter, we show that the observed number density $\approx 1/{\rm Mpc}^3$ of high-redshift galaxies in the HFF sets a lower limit $m_ψ\geq 8\cdot 10^{-22}$ eV (at 3-$σ$ confidence level) on the particle mass, a result that strongly disfavors wavelike bosonic Dark Matter as a viable model for structure formation. We discuss the impact on our results of uncertainties due to systematics in the selection of highly magnified, faint galaxies at high redshifts.

astro-ph.CO↗

arXiv2007

Semiclassical and Quantum Black Holes and their Evaporation, de Sitter and Anti-de Sitter Regimes, Gravitational and String Phase Transitions

An effective string theory in physically relevant cosmological and black hole space times is reviewed. Explicit computations of the quantum string entropy, partition function and quantum string emission by black holes (Schwarzschild, rotating, charged, asymptotically flat, de Sitter dS and AdS space times) in the framework of effective string theory in curved backgrounds provide an amount of new quantum gravity results as: (i) gravitational phase transitions appear with a distinctive universal feature: a square root branch point singularity in any space time dimensions. This is of the type of the de Vega - Sanchez transition for the thermal self-gravitating gas of point particles. (ii) There are no phase transitions in AdS alone. (iii) For $dS$ background, upper bounds of the Hubble constant H are found, dictated by the quantum string phase transition.(iv) The Hawking temperature and the Hagedorn temperature are the same concept but in different (semiclassical and quantum) gravity regimes respectively. (v) The last stage of black hole evaporation is a microscopic string state with a finite string critical temperature which decays as usual quantum strings do in non-thermal pure quantum radiation (no information loss).(vi) New lower string bounds are given for the Kerr-Newman black hole angular momentum and charge, which are entirely different from the upper classical bounds. (vii) Semiclassical gravity states undergo a phase transition into quantum string states of the same system, these states are duals of each other in the precise sense of the usual classical-quantum (wave-particle) duality, which is universal irrespective of any symmetry or isommetry of the space-time and of the number or the kind of space-time dimensions.

hep-th↗