We derive the Landau-Khalatnikov-Frandkin transformation (LKFT) for the fermion propagator in quantum electrodynamics (QED) described within a brane-world inspired framework where photons are allowed to move in $d_{\gamma }$ space-time (bulk) dimensions, while electrons remain confined to a $d_e$-dimensional brane, with $d_e<d_{\gamma }$, referred to in the literature as reduced quantum electrodynamics, ${\mathrm{RQED}}_{d_{\gamma },d_e}$. Specializing to the case of graphene, namely, ${\mathrm{RQED}}_{4,3}$ with massless fermions, we derive the nonperturbative form of the fermion propagator starting from its bare counterpart and then compare its weak coupling expansion to known one- and two-loop perturbative results. The agreement of the gauge-dependent terms at order $\alpha$ and ${\alpha }^2$ is reminiscent of the structure of LKFT in ordinary QED in arbitrary space-time dimensions and provides strong constraints for the multiplicative renormalizability of ${\mathrm{RQED}}_{d_{\gamma },d_e}$.

We construct the Barut–Girardello coherent states for charge carriers in anisotropic 2D-Dirac materials immersed in a constant homogeneous magnetic field which is orthogonal to the sample surface. For that purpose, we solve the anisotropic Dirac equation and identify the appropriate arising and lowering operators. Working in a Landau-like gauge, we explicitly construct nonlinear coherent states as eigenstates of a generalized annihilation operator with complex eigenvalues which depends on an arbitrary function f of the number operator. In order to describe the anisotropy effects on these states, we obtain the Heisenberg uncertainty relation, the probability density, mean energy value and occupation number distribution for three different functions f . For the case in which the anisotropy is caused by uniaxial strain, we obtain that when the stress is applied along the x -axis of the material surface, the probability density for the nonlinear coherent states is smaller compared to when the material is stressed along the orthogonal axis.

We calculate the complete one-loop off-shell three-point scalar-photon vertex in arbitrary gauge and dimension for scalar quantum electrodynamics. Explicit results are presented for the particular cases of dimensions 3 and 4 both for massive and massless scalars. We then propose nonperturbative forms of this vertex that coincide with the perturbative answer to order $e^2$.

In this work, we construct coherent states for electrons in anisotropic 2D Dirac materials immersed in a uniform magnetic field orthogonal to the sample. In order to describe the bidimensional effects on electron dynamics in a semiclassical approach, we adopt the symmetric gauge vector potential to describe the magnetic field. By solving a Dirac-like equation with an anisotropic Fermi velocity, we define two sets of generalized ladder operators that are generators of either the Heisenberg–Weyl or su (1,1) algebra and construct coherent states as eigenstates of the generalized annihilation operators with complex eigenvalues. In order to illustrate the anisotropy effects on these states, we obtain their probability density and mean energy value. Depending upon the anisotropy, expressed by the ratio between the Fermi velocities along the x - and y -axes, the shape of the probability density is modified on the xy -plane with respect to the isotropic case and according to the classical dynamics.

This study investigates the application of an artificial neural network (ANN) framework for analysing water pollution caused by solids. To address the challenge, we develop a convolutional neural network trained under a transfer learning strategy with AlexNet. We feed the network with pictures of samples of water with low, medium, and high concentrations of total suspended solids and achieve a high validation accuracy of 99.85% with a precision of 99.85%, which is highly competitive with other approaches. Our model demonstrates significant improvements in speed and reliability over conventional image processing methods, effectively predicting pollution levels. Our findings suggest that ANNs can serve as an effective tool for real-time monitoring and management of water pollution, facilitating proactive decision-making and policy formulation.