Modern Physics Letters A

This work attempts to investigate the influence of the linear and quadratic generalized uncertainty principle (LQGUP) on the thermodynamical characteristics of relativistic Fermi gas. The general thermodynamical characteristics of relativistic Fermi gas, such as mean energy, pressure, entropy, and specific heat, are obtained. According to the modified function of temperature for mean energy and specific heat of relativistic Fermi gas, we find that at high temperature limit, the value of deformation parameter in the framework of LQGUP has an important effect on thermodynamic characteristics. It appears that the deformation parameter’s value is rising at higher energy levels of science, resulting in the minimal measurable length reaching close to the Planck length scale.

In this paper, we show that loop-induced processes involving new physics particles can readily satisfy Landau Equation and trigger triangular singularities at high-energy colliders, leading to fully visible Standard Model final states. In addition, a t-channel triangular singularity can also occur during particle scattering processes that may extend to low momentum exchange. We discuss several typical scenarios in supersymmetric and extended Higgs models, and three types of final-state kinematic features at the collider. Four-particle vertices in new physics can play a significant role in high energy diagrams. We identify an “everything on shell” triangular singularity diagram only involving bosonic couplings, which has the potential to completely avoid large virtuality suppression. We further show that such a virtuality-free diagram is missing in the Standard Model at electroweak scale, and it becomes available in new physics models.

The stransverse mass variable $M_{T2}$ was originally proposed for the study of hadron collider events in which $N=2$ parent particles are produced and then decay semi-invisibly. Here we consider the generalization to the case of $N\ge 3$ semi-invisibly decaying parent particles. We introduce the corresponding class of kinematic variables $M_{\mathrm{\text{TN}}}$ and illustrate their mathematical properties. Many of the celebrated features of the $M_{T2}$ kinematic endpoint are retained in this more general case, including the ability to measure the mass of the invisible daughter particle from the stransverse mass kink. We describe and validate a numerical procedure for computing $M_{\mathrm{\text{TN}}}$ in practice. We also identify the configurations of visible momenta which result in nontrivial ($M_{\mathrm{\text{TN}}}\ne 0$) values, and derive a pure phase-space estimate for the fraction of such events for any N.

This study explores the interaction between non-extensive entropic FLRW cosmology and the power-law inflationary model, with a focus on the overlap between the scalar spectral index “$n_s$” and the tensor-to-scalar ratio “r”. Based on a conjecture that non-extensive entropy alters the energy–momentum content of the cosmic fluid, the analysis examines how these overlaps shift with different model parameters and compares the findings to those from Bekenstein–Hawking (BH) entropic cosmology. The study highlights the impact of Tsallis, Rényi, and Sharma–Mittal entropies, uncovering a significant correlation between “$n_s$” and “r” that suggests a deeper connection in power-law inflationary dynamics. The results demonstrate that non-extensive entropies not only enable viable inflation with a graceful exit but also address limitations inherent in the standard BH entropic framework, emphasizing the importance of precise parameter estimation. Specifically, Tsallis entropy allows for power-law inflation with $n=1$ to $n=2$ in alignment with Planck 2018 data. Moreover, the $\alpha$ parameter in Rényi and Sharma–Mittal entropy models must be extremely small ($\alpha \le 10^{-8}$ in Planck mass units) to achieve successful power-law inflation with an e-folding number around 55–65, suggesting a unified thermodynamic perspective in cosmological studies.

In this paper, we propose a nonlocal extension of the mimetic dark matter model based on the FALVA implementation of fractional calculus. Our primary objective to explore how certain properties of dark matter can be modeled within the FALVA framework rather than formulate a phenomenological model. We begin by constructing the action functional of the cosmological extension of the mimetic dark model and deriving the nonlinear equations of motion in the general case. Next, we focus on a fractional-power homogeneous mimetic dark field with an exponential expansion factor. We derive the equation of motion for the lapse field and obtain its general solution. Analytical solutions are then obtained for small time intervals and arbitrary values of the fractionality parameter. These solutions enable us to establish the physical line element of spacetime, incorporating the mimetic dark matter field. From this line element, we derive the Ricci tensor, Ricci scalar, and geodesic equations.

After a brief recount of small and large gauge transformations and the nature of observables, we discuss superselection sectors in gauge theories. There are an infinity of them, classified by large gauge transformations. Gauge theory sectors are labeled by the eigenvalues of a complete commuting set (CCS) of these transformations. In QED, the standard chemical potential is one such operator generating global U(1). There are many more given by the moments of the electric field on the sphere at infinity. In QCD, the CCS are constructed from the two commuting generators spanning a Cartan subalgebra. Large gauge transformations commute with the Hamiltonian and preserve the equations of motion. They form an infinite number of ‘classical symmetries’. But most of them are anamolous changing the superselection sectors. We show that any element of a large gauge transformation can be added to the standard Hamiltonian as a generalized chemical potential without changing field equations and that in QCD, they lead to confined and deconfined phases. A speculation about the physical meaning of these chemical potentials is also made.

In this paper, we extend the self-consistent quasi-particle model proposed by Zong et al. [Phys. Lett. B 711, 65 (2012)] to the case of finite magnetic field. The vacuum infinity zero-point energy is successfully eliminated by introducing a classical thermo-magnetic background field $B(T,eB)$ in the effective Lagrangian based on Zong’s method. By considering relativistic Landau energy levels, we have applied the improved quasi-particle model to the case of a two-flavor quark gluon plasma. We obtain a finite partition function and calculate the energy density, pressure and entropy density at zero chemical potential. These results are qualitatively consistent with the results of previous literature works.

It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars. Another crucial result is that the curvature scalars have singular behavior at certain points, and these singularities are not coordinate singularities. The nature of these singularities clearly points towards the idea of high-energetic probes turning into black holes. The absence of any such noncommutative corrections, and thus any such singularities, in the cases of Cartesian coordinates and cylindrical coordinates leads to the conclusion that high-energetic probes do not turn into black holes when the canonical NC structure is considered for these coordinates.

The bound state solutions of the Schrödinger equation (SE) under a deformed hyperbolic potential are used in this paper to investigate the correlation between the information content, such as Shannon entropies and Fisher information, and the variance of a quantum system in both momentum and position spaces. The variance was obtained from the expectation moments in conjugated spaces and used to get the uncertainty products, Fisher information products and Shannon entropic sums for different potential parameters. These information measures were observed to vary with the potential parameters and obey their lowest bound inequalities. An increase in the Fisher information leads to a lower uncertainty and less information while decreases in the Fisher information result in higher uncertainties. We proposed a relationship between the Shannon entropies, Fisher information and the variance where an increase in the Fisher information leads to a lower Shannon entropy or a lower spread of the probability distribution and vice versa. The numerical results obtained with the proposed relations agree with the most utilized method in the literature. This current work simplifies the calculation of the Shannon entropies notably for complex potential functions.

We analyze a recent calculation of the energy levels of some quantum-mechanical models derived from the so-called generalized Cornell potential. We argue that the authors obtained essentially the same spectrum for potentials with considerably different spectra. We show that the authors obtained negative eigenvalues in the case of a positive-definite potential. The reason is due to the approximation used in the solution of the Schrödinger equation. We point out that the omission of the sum over the rotational degrees of freedom in the canonical partition function leads to incomplete expressions for the thermodynamic functions.