Star Product Research Articles

Embedding space approach to Jackiw-Teitelboim gravity

We present a coordinate-free background space construction of Euclidean Jackiw-Teitelboim gravity. It is written as a gauge theory obtained from the Killing vectors and conformal Killing vectors of a hyperboloid embedded in a three-dimensional background. A novel feature of the gauge theory is that vanishing field strength does not necessarily imply that the gauge potentials (written in the embedding space) are pure gauges, not even locally. On the other hand, the projection of the potentials along the hyperboloid are pure gauges, as is the case in the standard approach. As is usual, metric tensors are dynamically generated from the classical solutions of the theory, which here do not rely on coordinate charts on the two-dimensional surface. We find a special class of solutions whereby the derived metric tensor on the surface is the induced metric from the background space. The gauge theory construction given here has a natural generalization to a noncommutative space, which does not require the use of coordinates, symbols, or a star product. Published by the American Physical Society 2024

How to expand the thermos cup market through network publicity and product positioning

With the steady growth of the global stainless steel thermos cup market, social platform marketing plays a key role in enhancing brand influence and product sales. Through the study of Standly's case, this paper first describes the strategy of making thermos cups into "fashion accessories", and Stanley has achieved remarkable market expansion by increasing the attention of female consumers; Then, the actual effect of this strategy is analyzed, that is, the sales volume of its star product Quencher series has increased greatly. Finally, suggestions on using new technologies and social media marketing are put forward to meet the needs of consumers and enhance brand influence. It is concluded that continuous innovation and optimization of market positioning are the key to maintain the leading position in the competition of vacuum flask industry. Research on marketing strategy is very important for enterprises to succeed in the rapidly changing market. It can not only help enterprises identify market opportunities and optimize resource allocation, but also meet customer needs, enhance brand influence, and ultimately promote the sustainable development and growth of enterprises.

Aumentando la productividad en una empresa panificadora

In a changing and competitive environment, companies must seek to increase the number of products withthe same resources, so this article has how to design different alternatives to increase productivity in the company "Charlotte Patisserie", first by carrying out a general investigation, then by doing data and analyzing them to culminate with the generation of the different improvement alternatives for the blueberry cheesecake star product, with the purpose of avoiding the interruption of work and optimizing the performance of the operators when collecting to prepare the desserts. The result obtained with the best alternative proposed was an increase in productivity of 12 % through the reduction of travel and operation times. ILIA: Investigaciones Latinoamericanas en Ingeniería y Arquitectura, No. 01, 2024: 155-158.

Type Ia Supernovae from First-generation Stars

Type Ia supernovae (SNe Ia) discovered at redshift z ≲ 2.5 are presumed to be produced from Population I/II stars. In this work, we investigate the production of SNe Ia from Population III binaries in the cosmological framework. We derive the SN Ia rate as a function of redshift in a theoretical context for the production of first-generation stars and evaluate the likelihood of their detection by the James Webb Space Telescope (JWST). Assuming the initial stellar mass function (IMF) favors low-mass stars, as from recent numerical simulations, we found that Population III stars may give rise to a considerable number of SNe Ia at high redshift, and Population III stars may even be the dominant SN Ia producer at z ≳ 6. In an optimistic scenario, we expect ∼1(2) SNe Ia from Population III stars at z ≈ 4(5) for a survey of area 300arcmin2 during a 3 yr period with JWST. The same survey may record more than ∼400 SNe Ia at lower redshift (z ≲ 2.5) but with only about one of them from Population III progenitors. There will be ∼six Population III SNe Ia in the same field of view at redshifts of 5–10. Observational constraints on SN Ia rates at the redshift range of 5–10 can place crucial constraints on the IMF of Population III stars.

Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff–Sagnotti counter-terms, and geometric flows

Nonassociative modifications of general relativity, GR, defined by star products with R-flux deformations in string gravity consist an important subclass of modified gravity theories, MGTs. A longstanding criticism for elaborating quantum gravity, QG, argue that the asymptotic safety does not survive once certain perturbative terms (in general, nonassociative and noncommutative) are included in the projection space. The goal of this work is to prove that a generalized asymptotic safety scenario allows us to formulate physically viable nonassociative QG theories using effective models defined by generic off-diagonal solutions and nonlinear symmetries in nonassociative geometric flow and gravity theories. We elaborate on a new nonholonomic functional renormalization techniques with parametric renormalization group, RG, flow equations for effective actions supplemented by certain canonical two-loop counter-terms. The geometric constructions and quantum deformations are performed for nonassociative phase spaces modelled as R-flux deformed cotangent Lorentz bundles. Our results prove that theories involving nonassociative modifications of GR can be well defined both as classical nonassociative MGTs and QG models. Such theories are characterized by generalized G. Perelman thermodynamic variables which are computed for certain examples of nonassociative geometric and RG flows.

A clinical trial evaluation of handwashing products and educational resources to improve hand hygiene in paediatric patients and school children.

It is widely acknowledged that good hand hygiene (HH) is an important non-pharmaceutical method for reducing the transmission of infectious diseases. Children are at high risk of infection due to their immature immune systems. Hospital transmitted infections are a cause for concern worldwide, with poor HH suggested to be responsible for up to 20% of cases. Patients, in particular paediatric patients, are often overlooked when it comes to the promotion of hand hygiene compliance (HHC) in hospitals. This report describes the clinical evaluation of the 'Soaper Stars'; a collection of child-friendly HH products with linked educational resource, developed using the COM-B approach to behaviour change, and designed to encourage correct HH in paediatric patients and in schools. The Soaper Star products were distributed on paediatric wards in five UK hospitals, and the use of the products around mealtimes was evaluated. Workshops teaching the 'why when and how' of handwashing were run in four UK primary schools with pre and post evaluations conducted to establish impact on knowledge. Over 300 children were involved. The Soaper Stars products stimulated a 38% increase in HHC compared to when only hospital-issued products were available, and verbal feedback from families indicated that having the Soaper Star products encouraged improved HHC by all visitors, not just the patient. Workshops in four schools (283 pupils) showed an increase in knowledge around the transmission of infection and the need for good HH that was sustained for at least 4 weeks. The results of this study demonstrate that providing children with the age-appropriate knowledge about why HH is necessary, and the child-friendly means to maintain their HH, will lead to greater HHC, not just by individual children, but also their families.

Beyond the Rotational Deathline: Radio Emission from Ultra-long Period Magnetars

ABSTRACT Motivated by the recent detection of ultralong-period radio transients, we investigate new models of coherent radio emission via low-altitude electron–positron pair production in neutron stars (NSs) beyond rotationally powered curvature radiation deathlines. We find that plastic motion (akin to ‘continental drift’) and qualitatively similar thermoelectric action by temperature gradients in the crusts of slowly rotating, highly magnetized NSs could impart mild local magnetospheric twists. Regardless of which mechanism drives twists, we find that particle acceleration initiates pair cascades across charge-starved gaps above a mild critical twist. Cascades are initiated via resonant inverse-Compton scattered photons or curvature radiation, and may produce broad-band coherent radio emission. We compute the pair luminosity (maximum allowed radio luminosity) for these two channels, and derive deathlines and ‘active zones’ in $P-\dot{P}$ space from a variety of considerations. We find these twist-initiated pair cascades only occur for magnetar-like field strengths $B \gtrsim 10^{14}$ G and long periods: $P_{\rm RICS} \gtrsim 120 \,\, (T/10^{6.5} {\rm K})^{-5} \, {\rm s}$ and $P_{\rm curv} \gtrsim 150 \,\, ({\rm v_{\rm pl}}/10^{3} {\, \rm cm \, yr^{-1}})^{-7/6} \, {\rm s}$. Using a simplified geometric model, we find that plastic motion or thermoelectrically driven twists might naturally reproduce the observed luminosities, time-scales, and timing signatures. We further derive ‘active zones’ in which rotationally powered pair creation occurs via resonantly scattered photons, beyond standard curvature deathlines for pulsars. All cascades are generically accompanied by simultaneous (non-)thermal X-ray/UV counterparts which might be detectable with current instrumentation.

Resurgence of Refined Topological Strings and Dual Partition Functions

We study the resurgent structure of the refined topological string partition function on a non-compact Calabi-Yau threefold, at large orders in the string coupling constant $g_s$ and fixed refinement parameter $\mathsf{b}$. For $\mathsf{b}\neq 1$, the Borel transform admits two families of simple poles, corresponding to integral periods rescaled by $\mathsf{b}$ and $1/\mathsf{b}$. We show that the corresponding Stokes automorphism is expressed in terms of a generalization of the non-compact quantum dilogarithm, and we conjecture that the Stokes constants are determined by the refined Donaldson-Thomas invariants counting spin-$j$ BPS states. This jump in the refined topological string partition function is a special case (unit five-brane charge) of a more general transformation property of wave functions on quantum twisted tori introduced in earlier work by two of the authors. We show that this property follows from the transformation of a suitable refined dual partition function across BPS rays, defined by extending the Moyal star product to the realm of contact geometry.

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.

Star exponentials from propagators and path integrals

In this paper we address the relation between the star exponentials emerging within the Deformation Quantization formalism and Feynman’s path integrals associated with propagators in quantum dynamics. In order to obtain such a relation, we start by visualizing the quantum propagator as an integral transform of the star exponential by means of the symbol corresponding to the time evolution operator and, thus, we introduce Feynman’s path integral representation of the propagator as a sum over all the classical histories. The star exponential thus constructed has the advantage that it does not depend on the convergence of formal series, as commonly understood within the context of Deformation Quantization. We include some basic examples to illustrate our findings, recovering standard results reported in the literature. Further, for an arbitrary finite dimensional system, we use the star exponential introduced here in order to find a particular representation of the star product which may be recognized as the one encountered in the context of the quantum field theory for a Poisson sigma model.

Supersymmetric Quantum Mechanics on a noncommutative plane through the lens of deformation quantization

A gauge invariant mathematical formalism based on deformation quantization is outlined to model an N=2 supersymmetric system of a spin 1/2 charged particle placed in a nocommutative plane under the influence of a vertical uniform magnetic field. The noncommutative involutive algebra (C∞(R2)[[ϑ]],∗r) of formal power series in ϑ with coefficients in the commutative ring C∞(R2) was employed to construct the relevant observables, viz., SUSY Hamiltonian H, supercharge operator Q and its adjoint Q† all belonging to the 2 × 2 matrix algebra M2(C∞(R2)[[ϑ]],∗r) with the help of a family of gauge-equivalent star products ∗r. The energy eigenvalues of the SUSY Hamiltonian all turned out to be independent of not only the gauge parameter r but also the noncommutativity parameter ϑ. The nontrivial Fermionic ground state was subsequently computed associated with the zero energy which indicates that supersymmetry remains unbroken in all orders of ϑ. The Witten index for the noncommutative SUSY Landau problem turns out to be −1 corroborating the fact that there is no broken supersymmetry for the model we are considering.

Schwarzschild black hole surrounded by a cavity and phase transition in the non-commutative gauge theory of gravity

In this work, we investigate the phase transition of the Schwarzschild black hole (SBH) inside an isothermal spherical cavity in the context of the non-commutative (NC) gauge theory of gravity, by using the Seiberg–Witten (SW) map and the star product. Firstly, we compute the NC correction to the Hawking temperature and derive the logarithmic correction to the entropy, then we derive the local temperature and local energy of NC SBH in isothermal cavity. Our results show that the non-commutativity removes the commutative divergence behavior of temperature, and prevents the SBH from the complete evaporation, which leads to a remnant black hole, and this geometry has predicted a minimal length in the order of Planck scale Θ∼lplanck. Therefore, the thermodynamic stability and phase transition is studied by analyzing the behavior of the local heat capacity and the Helmholtz free energy in the NC spacetime, where the results show that, the NC SBH has a two second-order phase transition and one first-order phase transition, with two Hawking–Page phase transition in the NC gauge theory.

Nonassociative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics

We elaborate on a model of nonassociative and noncommutative gauge gravity for the de Sitter gauge group SO(4,1) embedding extensions of the affine structure group Af(4,1) and the Poincaré group ISO(3,1). Such nonassociative gauge gravity theories are determined by star product R-flux deformations in string theory and can be considered as new avenues to quantum gravity and geometric and quantum information theories. We analyse physically important and geometric thermodynamic properties of new classes of generic off-diagonal cosmological solitonic solutions encoding nonassociative effective sources. Particularly, we focus on modelling by such solutions of locally anisotropic and inhomogeneous dark matter and dark energy structures generated as nonassociative solitonic hierarchies. Such accelerating cosmological evolution scenarios cannot be described in the framework of the Bekenstein–Hawking thermodynamic formalism. This motivates a change in the gravitational thermodynamic paradigm by considering nonassociative and relativistic generalizations of the concept of W-entropy in the theory of Ricci flows. Finally, we compute the corresponding modified G. Perelman’s thermodynamic variables and analyse the temperature-like evolution of cosmological constants determined by nonassociative cosmological flows.

Finite-element assembly approach of optical quantum walk networks

We present a finite-element approach for computing the aggregate scattering matrix of a network of linear coherent scatterers. These might be optical scatterers or more general scattering coins studied in quantum walk theory. While techniques exist for two-dimensional lattices of feed-forward scatterers, the present approach is applicable to any network configuration of any collection of scatterers. Unlike traditional finite-element methods in optics, this method does not directly solve Maxwell’s equations; instead it is used to assemble and solve a linear, coupled scattering problem that emerges after Maxwell’s equations are abstracted within the scattering matrix method. With this approach, a global unitary is assembled corresponding to one time step of the quantum walk on the network. After applying the relevant boundary conditions to this global matrix, the problem becomes non-unitary and possesses a steady-state solution that is the output scattering state. We provide an algorithm to obtain this steady-state solution exactly using a matrix inversion, yielding the scattering state without requiring a direct calculation of the eigenspectrum. The approach is then numerically validated on a coupled-cavity interferometer example that possesses a known, closed-form solution. Finally, the method is shown to be a generalization of the Redheffer star product, which describes scatterers on one-dimensional lattices (2-regular graphs) and is often applied to the design of thin-film optics, making the current approach an invaluable tool for the design and validation of high-dimensional phase-reprogrammable optical devices and study of quantum walks on arbitrary graphs.

Multidirectional cascade of square MIMO LTI subsystems: Transfer function representation

This paper considers continuous transfer function representation for a cascade composed of N mutually interconnected square multiple-input multiple-output (MIMO) linear time-invariant (LTI) subsystems with general multidirectional input–output configurations. Such cascaded structure can arise, e.g., from the spatial discretization of one-dimensional distributed parameter systems (DPSs) described by partial differential equations (PDEs) with boundary conditions representing different configurations of boundary input signals. As shown in the paper, the transfer function matrix of the resulting cascade can be calculated using the Redheffer star product of the subsystems’ transfer function matrices, which simplifies into the usual matrix product for the unidirectional cascade. For the particular case of 2 × 2 cascade composed of rational transfer function subsystems, the recursive formulas for its boundary and distributed transfer functions have been derived for both uni- and multidirectional configurations. The well-posedness and the stability criteria are also analyzed, proving to be more restrictive for the multidirectional cascade than for the unidirectional one due to the internal positive feedback in the first case. As shown in the attached example, the presented results can be used to approximate one-dimensional distributed parameter systems using rational transfer function subsystems representing the spatial sections of the original DPS.

Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom.

This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ2, where κ = (m/M)1/4 is the usual Born-Oppenheimer parameter. The lowest order term is the usual Born-Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born-Oppenheimer theory. We show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born-Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

Non-commutative gauge symmetry from strong homotopy algebras

We explicitly construct an L ∞ algebra that defines U ⋆(1) gauge transformations on a space with an arbitrary noncommutative and even nonassociative star product. Matter fields are naturally incorporated in this scheme as L ∞ modules. Some possibilities for including P ∞ algebras are also discussed.

Sirt3 Regulates Proliferation and Progesterone Production in Leydig Cells via Suppression of Reactive Oxygen Species.

Sirt3 is a mitochondrial protein deacetylase functioning in energy metabolism, regulation of intracellular reactive oxygen species (ROS) levels, and aging. Although Sirt3 loss has negative effects on fertility of oocytes during in vitro fertilization and on progesterone production in granulosa cells, Sirt3's function in Leydig cells remains unclear. Therefore, we investigated Sirt3 activity in Leydig cells, focusing on androgen production. To do so, we performed immunohistochemistry to confirm Sirt3 localization in gonads and observed strong Sirt3 immunostaining in Leydig cells of human testes and of Sirt3+/+ and Sirt3+/- mouse testes, while Sirt3-/- mouse testis tissue was negative. In human ovary, hilus cells were strongly Sirt3-positive, theca cells showed weak positivity, and granulosa cells showed very weak or almost no immunostaining. Next, we used the murine Leydig tumor cell line MA-10 as a model. We overexpressed Sirt3 but observed no changes in proliferation, expression of Star, Cyp11a1 (p450scc gene), and Hsd3b, or progesterone production in MA-10 cells. Sirt3 knockdown significantly reduced proliferation, suppressed expressions of steroidogenic enzymes and of transcription factors Ad4bp (Sf-1 gene) and Gata4, and decreased progesterone production. Sirt3 knockdown in MA-10 cells also increased intracellular ROS levels based on CM-H2DCFDA fluorescence dye analysis and increased the proportion of both early and late apoptotic (necrotic) cells based on Annexin V/7AAD assays. These results indicate that Sirt3 has a potential function in androgen production in Leydig cells by regulating intracellular ROS levels.

3D NLTE Lithium abundances for late-type stars in GALAH DR3

ABSTRACT Lithium’s susceptibility to burning in stellar interiors makes it an invaluable tracer for delineating the evolutionary pathways of stars, offering insights into the processes governing their development. Observationally, the complex Li production and depletion mechanisms in stars manifest themselves as Li plateaus, and as Li-enhanced and Li-depleted regions of the HR diagram. The Li-dip represents a narrow range in effective temperature close to the main-sequence turn-off, where stars have slightly super-solar masses and strongly depleted Li. To study the modification of Li through stellar evolution, we measure 3D non-local thermodynamic equilibrium (NLTE) Li abundance for 581 149 stars released in GALAH DR3. We describe a novel method that fits the observed spectra using a combination of 3D NLTE Li line profiles with blending metal-line strength that are optimized on a star-by-star basis. Furthermore, realistic errors are determined by a Monte Carlo nested sampling algorithm which samples the posterior distribution of the fitted spectral parameters. The method is validated by recovering parameters from a synthetic spectrum and comparing to 26 stars in the Hypatia catalogue. We find 228 613 Li detections, and 352 536 Li upper limits. Our abundance measurements are generally lower than GALAH DR3, with a mean difference of 0.23 dex. For the first time, we trace the evolution of Li-dip stars beyond the main sequence turn-off and up the subgiant branch. This is the first 3D NLTE analysis of Li applied to a large spectroscopic survey, and opens up a new era of precision analysis of abundances for large surveys.

Gaining From Losing a Competition in Product Variety

This article studies the impact of a competing firm's substantial expansion in product variety, achieved through modularity and delayed differentiation, on the sales and inventory of the focal firm in the market. Intuitively, the firm's sales are expected to decrease when a competitor increases its product variety, as existing consumers are drawn to the greater range of competing products, resulting in a substitution effect. However, we also emphasize a simultaneous spillover effect, where the dramatic increase in a competitor's product variety can expand the overall market for all firms (including the focal firm) by attracting new consumers to the market. The net impact thus depends on the tradeoff between the substitution effect and spillover effect, forming an empirical question. To explore this tradeoff and quantify the net impact of a competitor's substantial increase in product variety on the focal firm's sales and inventory, we exploit the launch of Coca-Cola's Freestyle dispenser that offers over 120 beverage products via modularity and delayed differentiation. Our analysis focuses on the treatment effects of the launch of Freestyle on changes in the focal firm's sales quantity, sales dispersion, and inventory levels. Contrary to common intuition, we find that the focal firm's total sales remain unchanged following the launch of Freestyle dispensers, but its sales dispersion increases by 2.2%, which in turn leads to a 1.0% increase in inventory levels at distribution centers. The unchanged total sales and increased sales dispersion imply a redistribution of sales among the focal firm's stock keeping units (SKUs). By analyzing data at the SKU level and the business customer level, we uncover the mechanism behind this sales re-allocation: a 1.9% increase in the sales of the focal firm's long-tail products at the expense of its star product sales. Meanwhile, we identify a 0.9% increase in sales to retailers and entertainment locations, while sales to restaurants decline. These empirical results help disentangle the substitution and spillover effects on the focal firm's sales resulting from its competitor's substantially increased product variety. Managerial implications derived from these findings are discussed.