We propose a photonic scheme for analog quantum simulation of a $U(1)$ Lattice Gauge Theory (LGT) with dynamical matter based on the Jaynes-Cummings-Hubbard (JCH) model. Here, an array of interacting cavities in the strong-coupling regime of cavity Quantum Electrodynamics is mapped onto the alternating matter and gauge-field sites of the spin-1/2 Quantum Link Model. In contrast to other analog LGT quantum simulation methods, our approach implements the desired gauge-invariant dynamics through the hopping of polaritonic excitations among the array sites. The hopping is mapped to the gauge theory via precise tuning of polaritonic resonances in individual cavities. Using exact diagonalization, we show that the real-time evolution of the JCH model accurately replicates that of a Quantum Link Model. Finally, we discuss feasible routes to the beyond-classical simulation capability with scalable implementations in photonic and superconducting systems. This provides a novel route towards understanding the real-time dynamics of lattice gauge theories with matter in higher dimensions.

In this contribution to the Encyclopedia of Nuclear Physics, we aim to provide a pedagogical introduction to the functional approach to QCD at finite temperature and chemical potential. We briefly outline the general framework and address its complementarity to other first-principle approaches to non-perturbative QCD. We discuss selected results obtained with Dyson-Schwinger equations (DSE) and the functional renormalisation group (fRG) in the context of a general physics perspective on the QCD phase diagram. This article is specifically aimed at students and non-practitioners of functional methods alike and may serve as a short guide to further literature.

We perform an analysis of LQCD light - charmed (pseudoscalar) meson scattering data with UChPT for pion masses ranging from $m_\pi\simeq 230$~MeV till the SU(3) limit, $m_\pi\simeq 700$~MeV. We find two poles in the non-strange isospin $I=1/2$ sector that can be related to the experimental $D_0(2300)$ resonance. At the physical pion mass, the poles are located at $\sqrt{s_0}=2094(7)(1)-i111(7)(13)$ MeV, and $2463(60)(30)-i108(14)(12)$~MeV. While the first pole, named here $D_0^*(2100)$, is always a resonance in $D\pi$ within the $1\sigma$ region, the second pole can be a resonance or virtual state close to the $D\eta, D_s\bar{K}$ thresholds. For the first time, the pion mass dependence on different chiral trajectories including SU(3) LQCD data are investigated for these poles. We find that in the $m_s=m_{s,\mathrm{phy}}$ trajectory, the $D_0^*(2100)$ resonance pole behaves similarly as the $\sigma$ resonance in $\pi\pi$ scattering, splitting into two poles, connected to the $\bar{\mathbf{3}}$ representation. Moreover, we found that the higher pole related to the experimental $D_0^*(2300)$ can be related to the $\mathbf{6}$ representation. We highlight that since this pole couples strongly to channels with hidden strangeness, its mass is fairly constant in the $\mathrm{Tr}[M]=C$ trajectory, what can be tested in future LQCD simulations. The compositeness of the $D_0^*(2100)$ state at the SU(3) limit is evaluated. Finally, other sectors are also discussed.

Studying phase transitions in interacting quantum field theories generally requires the numerical study of the dynamical system on a large lattice, which is, in most cases, computationally very challenging. In this work an alternative method is proposed to solve Euclidean path integrals in quantum field theories, using radial basis function-type neural networks. The method allows us to approximate observables in a very efficient manner, taking only seconds to do calculations that would otherwise take hours or even days with other existing methods. The model is used to describe phase transitions in the scalar $\phi^4$ theory for a wide range of coupling strength. The obtained phase transition line is compared to previous lattice results, giving very good agreement between them.

We develop a generative framework based on denoising diffusion for the model-independent reconstruction of hadronic form factors from sparse and noisy data. The generative prior is built from a large ensemble of synthetic curves drawn from ten distinct functional classes rooted in different theoretical approaches to hadron structure. Applied to the proton gravitational form factors $A(t)$, $J(t)$, and $D(t)$, the framework yields non-parametric reconstructions consistent with lattice QCD across the full kinematic range $0\le -t\le 2~\mathrm{GeV}^{2}$, remaining robust even when only one or two conditioning points are retained. The densely sampled output enables a direct extraction of the chiral low-energy constants $c_8=-4.6\pm 0.8~\mathrm{GeV}^{-1}$ and $c_9=-0.61\pm 0.19~\mathrm{GeV}^{-1}$. Using these values at the physical pion mass, we obtain $D(0)=-4.3\pm 0.8$ for the nucleon $D$-term.