Search Results (460)

Research at the intersection of quantum gravity and quantum information theory has seen significant success in describing the emergence of spacetime and gravity from quantum states whose entanglement entropy approximately obeys an area law. In a different direction, the Kaluza–Klein proposal aims to recover gauge symmetries by means of dimensional reduction in higher-dimensional gravitational theories. Integrating both of these, gravitational and gauge degrees of freedom in $3+1$ dimensions may be obtained upon dimensional reduction in higher-dimensional emergent gravity. To this end, we show that entangled systems of two and three qubits can be associated with $5+1$- and $9+1$-dimensional spacetimes, respectively, which are reduced to $3+1$ dimensions upon singling out a preferred complex direction. Depending on the interpretation of the residual symmetry, either the Standard Model gauge group, $SU\left(3\right)\times SU\left(2\right)\times U\left(1\right)/{\mathbb{Z}}_6$, or the symmetry of Minkowski spacetime together with the gauge symmetry of a right-handed ‘half-generation’ of fermions can be recovered. Thus, there seems to be a natural way to accommodate the chirality of the weak force in the given construction. This motivates a picture in which spacetime emerges from the area law contribution to the entanglement entropy, while gauge and matter degrees of freedom are obtained due to area-law-violating terms. Furthermore, we highlight the possibility of using this construction in quantum simulations of Standard Model fields. Full article

Non-relativistic quantum mechanics was originally formulated to describe particles. Using ideas from the geometric quantization approach, we show how the concept of antiparticles can and should be introduced in the non-relativistic case without appealing to quantum field theory. We discuss this in detail using the example of the one-dimensional harmonic oscillator. Full article

Parental and peer support has been documented as an important factor in physical activities among high school students. Likewise, coach support has an important impact on physical activity among high school students. Meanwhile, many studies show that basic psychological needs have an essential effect on perceived autonomy and physical activity. As such, this study, using self-determination theory, aimed to explore the mediating role of basic psychological needs on physical activity among high school students in China. The Sport Climate Questionnaire, Psychological Need Satisfaction in Exercise Scale—Physical Activity, and the three-item Physical Activity Rating Scale-3 were employed to gauge responses from 736 high school students (15–18 years old). A structural equation model was employed to test the mediating effect. The researchers found a significant positive effect of perceived coach support on basic psychological need satisfaction. Basic psychological need satisfaction was also found to be a significant predictor of physical activity. Surprisingly, the results showed that perceived coach support negatively influences physical activity. As such, an indirect mediating effect is established. Basic psychological needs had an indirect mediating effect and could reduce the negative effect of coach support on physical activity engagement. Full article

Using a Dyson–Schwinger approach, we perform an analysis of the non-trivial ground state of thermal $SU\left(N\right)$ Yang–Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic observables such as energy density and pressure are derived analytically, using Jacobi elliptic functions. The results are compared with the lattice results. Good agreement is found at low temperatures, providing a viable scenario for a gas of massive glue states populating higher levels of the spectrum of the theory. At high temperatures, a scenario without glue states consistent with a massive scalar field is observed, showing an interesting agreement with lattice data. The possibility is discussed that the results derived in this analysis open up a novel pathway beyond lattice to precision studies of phase transitions with false vacuum and cosmological relics that depend on the equations of state in strong coupled gauge theories of the type of Quantum Chromodynamics (QCD). Full article

In recent years, the increasing use of mulching in agricultural practices has been driven by its benefits in weed suppression, soil moisture retention, and improved soil structure. However, Korean farms typically perform mulching and soil covering separately, leading to excessive labor requirements. To address this issue, this study analyzes the safety of a newly developed mulching and soil covering machine. To evaluate its structural safety, strain gauges were attached to critical points of the machine, and strain data were collected under various Power Take-Off (PTO) and engine speed conditions. The measured strain was converted into von Mises stress and maximum shear stress, and the safety factor was calculated using the maximum shear stress theory and the strain energy theory. Additionally, fatigue life was predicted using the rainflow counting method, the Goodman equation, and Palmgren–Miner’s rule. The results indicate that the safety factor ranged from 1.65 to 16.54 based on the maximum shear stress theory and 2.42 to 19.83 based on the strain energy theory, confirming that the machine can withstand operational loads without failure. Furthermore, fatigue life prediction revealed that the lowest estimated fatigue life is 14,575 h, equivalent to approximately 607 years of continuous use. These findings demonstrate that the developed machine possesses high safety, making it a viable solution for improving efficiency in mulching and soil covering operations. Full article

This paper explores the third-order nonlinear coupled KdV equation utilizing prolongation structure theory and gauge transformation. By applying the prolongation structure method, we obtained an extended version of the equation. Starting from the Lax pairs of the equation, we successfully derived the corresponding Darboux transformation and Bäcklund transformation for this equation, which are fundamental to our solving process. Subsequently, we constructed and calculated the recursive operator for this equation, providing an effective approach to tackling complex problems within this domain. These results are crucial for advancing our understanding of the underlying principles of soliton theory and their implications on related natural phenomena. Our findings not only enrich the theoretical framework but also offer practical tools for further research in nonlinear wave dynamics. Full article

Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many other methods, with tools coming from statistical mechanics lattice models, such as mean field methods, which are often used to provide approximate results. Applying these methods to LGTs requires particular attention due to the intrinsic local nature of gauge symmetry, how it is reflected in the variables used to formulate the theory, and the breaking of gauge invariance when approximations are introduced. This issue has been addressed over the decades in the literature, yielding different conclusions depending on the formulation of the theory under consideration. In this article, we focus on the mean field theoretical approach to the analysis of GTs and LGTs, connecting both older and more recent results that, to the best of our knowledge, have not been compared in a pedagogical manner. After a brief overview of mean field theory in statistical mechanics and many-body systems, we examine its application to pure LGTs with a generic compact gauge group. Finally, we review the existing literature on the subject, discussing the results obtained so far and their dependence on the formulation of the theory. Full article

This paper presents a novel approach to solving the Yang–Mills existence and mass gap problem using quantum information theory. We develop a rigorous mathematical framework that reformulates the Yang–Mills theory in terms of quantum circuits and entanglement structures. Our method provides a concrete realization of the Yang–Mills theory that is manifestly gauge-invariant and satisfies the Wightman axioms. We demonstrate the existence of a mass gap by analyzing the entanglement spectrum of the vacuum state, establishing a direct connection between the mass gap and the minimum non-zero eigenvalue of the entanglement Hamiltonian. Our approach also offers new insights into non-perturbative phenomena such as confinement and asymptotic freedom. We introduce new mathematical tools, including entanglement renormalization for gauge theories and quantum circuit complexity measures for quantum fields. The implications of our work extend beyond the Yang–Mills theory, suggesting new approaches to quantum gravity, strongly coupled systems, and cosmological problems. This quantum information perspective on gauge theories opens up exciting new directions for research at the intersection of quantum field theory, quantum gravity, and quantum computation. Full article

Fundamentally, duality gives two different points of view of looking at the same object. It appears in many subjects in mathematics (geometry, algebra, analysis, PDEs, Geometric Measure Theory, etc.) and in physics. For example, Connections on Fiber Bundles in mathematics, and Gauge Fields in physics are exactly the same. In n-dimensional geometry, a fundamental notion is the “duality” between chains and cochains, or domains of integration and the integrands. In this paper, we extend ideas given in our earlier articles and connect seemingly unrelated areas of F-harmonic maps, f-harmonic maps, and cohomology classes via duality. By studying cohomology classes that are related with p-harmonic morphisms, F-harmonic maps, and f-harmonic maps, we extend several of our previous results on Riemannian submersions and p-harmonic morphisms to F-harmonic maps and f-harmonic maps, which are Riemannian submersions. Full article

Alternative scenarios where the Big Bang singularity of the standard cosmological model is replaced by a bounce, or by an early almost static phase (known as emergent universe) have been frequently studied. We investigate the role of the spinor degrees of freedom in overcoming the initial singularity. We introduce a model which generalizes the Einstein–Cartan–Dirac theory, including local phase invariance of the spinor field supported by a gauge scalar field and certain couplings to the torsion. A natural gauge choice reduces the field equations to that of the Einstein–Dirac theory with a Dirac field potential that has polar and axial spinor currents. We identify a new potential term proportional to the square of the ratio of Dirac scalar and axial scalar, which provides a dark energy contribution dominating in the late-time Universe. In addition, the presence of spinor currents in the potential may induce the bounce of a contracting universe. Full article

This is a review/research paper on anomalies applied in a bottom–up approach to standard model and gravity. It is divided into two parts. The first consists of a proper review of anomalies in quantum field theories. Anomalies are analyzed according to three different methods: a perturbative one based on a Feynman diagram, a non-perturbative one relying on the Schwinger–DeWitt approach, and, third, one hinging on the Atiyah–Singer family’s index theorem. The three methods are applied both to chiral gauge anomalies and trace anomalies. The fundamental distinction, which our presentation leads to, is between obstructive (O) and non-obstructive (NO) anomalies. The former is tied to the non-existence of fermion propagators, which fatally maim the corresponding theory. In the second part, we apply this analysis to the SM and a variety of its extensions, which are immersed in a gravitational background, and we find that they are all plagued by a residual chiral trace anomaly. To completely eliminate all kinds of dangerous anomalies in SM-like theories, we propose a somewhat unconventional scheme and exemplify it by means of an explicit model. The latter is a left–right symmetric model. We embed it in a Weyl geometry to render it a conformal invariant. We then deal with some of its quantum aspects, particularly its even (NO) trace anomalies and the means to preserve its conformal invariance at the quantum level. We briefly review renormalization and unitarity in the framework of similar models discussed in the existing literature. Finally, we present a possible (conjectural) application of the model to describe the junction between cosmology and quantum field theory. Full article

This is the Part III paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework for the gauge-invariant perturbation theory and the proposal for gauge-invariant treatments of $l=0,1$ mode perturbations on the Schwarzschild background spacetime in the Part I paper, we examine the problem of whether the $l=0,1$ even-mode solutions derived in the Part II paper are physically reasonable. We consider the linearized versions of the Lemaître–Tolman–Bondi solution and the non-rotating C-metric. As a result, we show that our derived even-mode solutions to the linearized Einstein equations realize these two linearized solutions. This supports the conclusion that our derived solutions are physically reasonable, which implies that our proposal for gauge-invariant treatments of $l=0,1$ mode perturbations is also physically reasonable. We also briefly summarize the conclusions of our series of papers. Full article

This study proposes the design of a hybrid reluctance-actuated fast steering mirror (HRAFSM) using Maxwell’s electromagnetic normal stress principle. Strain gauges were attached to the flexible supports as sensors for measuring the rotation angles. According to Maxwell’s stress tensor theory and the theory of vibration mechanics, we obtained the dynamic equation of the HRAFSM in the uniaxial direction to investigate the relationship between the input current and the output angle of the entire system. Further, we propose a control algorithm combining proportional-integral-derivative (PID) and adaptive inverse control (AIC) to achieve high-precision control. We established an experimental system for testing and validation of the control method. The experimental results showed that the designed HRAFSM can achieve the expected rotation angle of ±1.5 mrad, and revealed a linear relationship between the rotation angle of the two axes and their corresponding strain voltages. The effectiveness of the designed controller was verified, and the amplitude tracking errors of the x- and y-axes were 0.1% and 0.14%, respectively. Full article

This is the Part II paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal of gauge-invariant treatments for $l=0,1$-mode perturbations on the Schwarzschild background spacetime in the Part I paper, we examine the linearized Einstein equations for even-mode perturbations. We discuss the strategy to solve the linearized Einstein equations for these even-mode perturbations including $l=0,1$ modes. Furthermore, we explicitly derive the $l=0,1$-mode solutions to the linearized Einstein equations in both the vacuum and the non-vacuum cases. We show that the solutions for $l=0$-mode perturbations includes the additional Schwarzschild mass parameter perturbation, which is physically reasonable. Then, we conclude that our proposal of the resolution of the $l=0,1$-mode problem is physically reasonable due to the realization of the additional Schwarzschild mass parameter perturbation and the Kerr parameter perturbation in the Part I paper. Full article