arXiv subjects

Rodrigo Carmo Terin

Publications and source records attributed to Rodrigo Carmo Terin.

15 recordsLinked to original sources

arXiv2026

A regulated zero-temperature construction of the Fundamental Modular Region in pure Yang--Mills theory and QCD

We formulate the Fundamental Modular Region (FMR) as the zero-temperature limit of regulated copy-weighted Landau gauges. At finite $β$, the measure localizes on absolute minima, and the leading correction is dominated by the inverse Faddeev--Popov (FP) operator. A small $SU(2)$ benchmark provides a computational realization through population annealing and collective basin hopping. Our construction defines absolute Landau gauge without parametrizing the FMR boundary and extends naturally to full quantum chromodynamics (QCD). It also admits a Hamiltonian interpretation in terms of the gauge-fixed vacuum wave functional on the FMR.

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arXiv2026

Neural solutions of coupled ghost and gluon Dyson--Schwinger equations in Landau gauge

The coupled ghost and gluon Dyson--Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang--Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.

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arXiv2026

Spectral functions in Minkowski quantum electrodynamics from neural reconstruction

We study neural reconstructions of quenched rainbow quantum electrodynamics (QED) Dyson--Schwinger benchmarks in Minkowski-related kinematics. Using the dispersive formulation as motivation, we separate the Euclidean Fukuda--Kugo equation, the spectral unitary equations, and the modified unitary equations. The Fukuda--Kugo benchmark is solved directly and shows the expected zero crossing above the critical region $α_c=π/3$. Neural reconstructions with free output reproduce this behavior, while positivity-constrained ansätze fail in the supercritical regime. Thus, spectral positivity should be treated as a diagnostic of the Lehmann representation, not imposed blindly as a neural constraint.

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arXiv2026

Quark sector effects and glueball mass sensitivity estimates in Lorentz-violating supersymmetric QCD-like theories

The $N=1$ supersymmetric Yang--Mills--Carroll--Field--Jackiw (SYM--CFJ) model is extended to include the quark sector of supersymmetric quantum chromodynamics (SQCD) in the presence of Lorentz--symmetry violation (LSV). The Lorentz--violating data are carried by a spurion chiral superfield whose components define a purely spacelike background vector $v_μ$ and fermionic bilinears, inducing a topological mass scale in the gauge sector. Working within a spurion effective field theory (EFT) and a small--LSV expansion, we classify the allowed parametric dependence of glueball observables on the induced mass scales. Using lattice Yang--Mills (YM) glueball masses only as a reference hadronic scale, we provide parametric sensitivity estimates and naturalness ranges for the topological mass $|v|$ relative to $Λ_{\rm YM}$.

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arXiv2026

Emergent Gribov horizon kernel from replica symmetry breaking in Yang--Mills theories

We show that, in the replica-broken sector of the Serreau--Tissier (ST) gauge fixing, the expansion of the replica determinant in the regulator $ζ$ induces a nonlocal bilinear gluonic kernel with the same color and Lorentz structure as the quadratic part of the BRST-invariant Gribov horizon functional. This establishes an effective leading-order correspondence with the refined Gribov-Zwanziger (RGZ) horizon sector, rather than a reconstruction of the full nonlinear functional $H(A^h)$. The induced scale satisfies $γ_{\mathrm{ind}}^4\propto ζ$ at leading order, up to scheme-dependent normalization and higher-order corrections. Depending on the replica phase, the ST sector yields either a local Curci--Ferrari (CF) screening mass or an induced RGZ-type horizon kernel, avoiding double counting of infrared scales.

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arXiv2026

Neuro-evolutionary stochastic architectures in gauge-covariant neural fields

We extend our gauge-covariant stochastic neural-field framework by promoting architecture-level parameters to slow stochastic variables evolving in function space. Our effective theory is formulated in terms of classical commuting fields and provides symmetry-constrained diagnostics of marginality and finite-width effects through the maximal Lyapunov exponent, the amplification factor, and dressed spectral kernels. On top of this dynamics, we introduce a Markovian evolutionary scheme compatible with the local $U(1)$ structure of the effective model. By using a minimal implementation, the genotype is reduced to the weight-variance parameter $σ_w^2$, and the fitness functional combines spectral agreement, marginal stability, and a symmetry-constrained critical anchor. Comparing three evolutionary models, we find that only the fully symmetry-constrained Ginibre $U(1)$ version robustly approaches a narrow near-marginal regime and reproduces the predicted low-frequency finite-width spectral behavior. These results support the use of symmetry-guided effective stability diagnostics as practical principles for stochastic architecture search in controlled settings.

cs.NE↗

arXiv2026

Gauge-covariant stochastic neural fields: Stability and finite-width effects

We develop a gauge-covariant stochastic effective field theory for stability and finite-width effects in deep neural systems. The model uses classical commuting fields: a complex matter field, a real Abelian connection field, and a fictitious stochastic depth variable. Using the Martin--Siggia--Rose--Janssen--de~Dominicis formalism, we derive its functional representation and a two-replica linear-response construction defining the maximal Lyapunov exponent and the amplification factor for the edge of chaos. Finite-width effects appear as perturbative corrections to dressed kernels, and the marginality condition remains unchanged at the order considered for fixed kernel geometry. Numerically, finite-width multilayer perceptrons follow the mean-field instability threshold, and a linear stochastic effective sector reproduces the predicted low-frequency spectral deformation.

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arXiv2026

Scale redundancy and soft gauge fixing in positively homogeneous neural networks

Neural networks with positively homogeneous activations exhibit an exact continuous reparametrization symmetry: neuron-wise rescalings generate parameter-space orbits along which the input--output function is invariant. We interpret this symmetry as a gauge redundancy and introduce gauge-adapted coordinates that separate invariant and scale-imbalance directions. Inspired by gauge fixing in field theory, we introduce a soft orbit-selection (norm-balancing) functional acting only on redundant scale coordinates. We show analytically that it induces dissipative relaxation of imbalance modes to preserve the realized function. In controlled experiments, this orbit-selection penalty expands the stable learning-rate regime and suppresses scale drift without changing expressivity. These results establish a structural link between gauge-orbit geometry and optimization conditioning, providing a concrete connection between gauge-theoretic concepts and machine learning.

cs.LG↗

arXiv2026

Glueball mass from RGZ-inspired infrared gluodynamics: a Euclidean Bethe-Salpeter approach

We formulate and solve a Euclidean Bethe-Salpeter equation for the lightest scalar glueball (0++) in pure Yang-Mills theory, using the refined Gribov-Zwanziger gluon tree-level propagator as an infrared-complete input. In a minimal ladder truncation with an effective constant kernel strength g_C^2 and the dominant s-wave component, we extract scalar glueball masses in the range 1.7-2.3 GeV for representative values of g_C^2, with a preferred value around 1.9 GeV near g_C^2 = 0.54. The result is consistent with RGZ correlator-based infrared moment analyses and with lattice expectations, providing a cross-check of RGZ-inspired infrared gluodynamics from a bound-state viewpoint.

hep-ph↗

arXiv2025

Towards a unified viewpoint of Gribov--Zwanziger and Serreau--Tissier gauge fixing

We investigate a unified Landau--gauge fixing that continuously interpolates between the viewpoints of the Serreau--Tissier (ST) copy-averaged formulation and the (Refined) Gribov--Zwanziger (RGZ) restriction to the first Gribov region. By combining the ST weight with a GZ-type horizon term and localizing both through the replica trick and the BRST-invariant $A_μ^h$ formulation, we obtain a single, local, BRST-invariant, power-counting renormalizable action. Algebraic renormalization shows that all counterterms are reabsorbed by a common set of field and parameter renormalizations, therefore the unification is algebraic rather than merely additive. The replica sector yields a radiatively generated gluon screening mass, while the RGZ parameters are fixed by the horizon and condensate gap equations; we also give infrared matching conditions that link both descriptions at small momentum. We present a compact BRST-superspace rewriting of the RGZ block and a simple hybrid superspace that hosts the ST replicas and RGZ side by side; these add no dynamics and organize the Ward-identity analysis. The resulting gluon propagator interpolates among the massive Faddeev--Popov--ST and the RGZ decoupling forms. This framework offers a controlled way to study how infrared Yang--Mills correlators depend on the balance between copy averaging and horizon suppression, and it suggests practical lattice tests through tunable copy weighting.

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arXiv2025

Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics

Physics-informed neural networks (PINNs) are employed to solve the Dyson--Schwinger equations of quantum electrodynamics (QED) in Euclidean space, with a focus on the non-perturbative generation of the fermion's dynamical mass function in the Landau gauge. By inserting the integral equation directly into the loss function, our PINN framework enables a single neural network to learn a continuous and differentiable representation of the mass function over a spectrum of momenta. Also, we benchmark our approach against a traditional numerical algorithm showing the main differences among them. Our novel strategy, which is expected to be extended to other quantum field theories, is the first step towards forefront applications of machine learning in high-level theoretical physics.

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arXiv2024

Generating and analyzing small-size datasets to explore physical observables in quantum Ising systems

We propose a detailed analysis of datasets generated from simulations of two-dimensional quantum spin systems using the quantum Ising model at absolute zero temperature. Our focus is on examining how fundamental physical properties, energy, magnetization, and entanglement entropy, evolve under varying external transverse magnetic fields and system sizes. From the Quantum Toolbox in Python (QuTiP), we simulate systems with 4, 8, and 16 spins arranged in square lattices, generating extensive datasets with 5000 samples per magnetic field value. The Hamiltonian operator incorporates quantum mechanical effects such as superposition and tunneling, challenging classical interpretations of spin states. We compute extended Pauli operators and construct the Hamiltonian to include spin-spin interactions and transverse field terms. Our analysis reveals that as the system size increases, fluctuations in energy and entanglement entropy become more evident, indicating lifted sensitivity to external perturbations and suggesting the onset of quantum phase transitions. Spin-spin correlation functions demonstrate that interactions are predominantly local, but larger systems exhibit more complex and fluctuating correlations. These findings provide valuable insights into the behavior of quantum spin systems and lay the groundwork for future machine learning applications aimed at predicting physical quantities and identifying phase transitions from a quantum perspective.

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arXiv2024

Identifying phase transitions in physical systems with neural networks: a neural architecture search perspective

The use of machine learning algorithms to investigate phase transitions in physical systems is a valuable way to better understand the characteristics of these systems. Neural networks have been used to extract information of phases and phase transitions directly from many-body configurations. However, one limitation of neural networks is that they require the definition of the model architecture and parameters previous to their application, and such determination is itself a difficult problem. In this paper, we investigate for the first time the relationship between the accuracy of neural networks for information of phases and the network configuration (that comprises the architecture and hyperparameters). We formulate the phase analysis as a regression task, address the question of generating data that reflects the different states of the physical system, and evaluate the performance of neural architecture search for this task. After obtaining the optimized architectures, we further implement smart data processing and analytics by means of neuron coverage metrics, assessing the capability of these metrics to estimate phase transitions. Our results identify the neuron coverage metric as promising for detecting phase transitions in physical systems.

cs.NE↗

arXiv2023

Looking at QED with Dyson-Schwinger equations: basic equations, Ward-Takahashi identities and the two-photon-two-fermion irreducible vertex

A minimal truncated set of the integral Dyson-Schwinger equations, in Minkowski spacetime, that allows to explore QED beyond its perturbative solution is derived for general linear covariant gauges. The minimal set includes the equations for the fermion and photon propagators, the photon-fermion vertex, and the two-photon-two-fermion one-particle-irreducible diagram. If the first three equations are exact, to build a closed set of equations, the two-photon-two-fermion equation is truncated ignoring the contribution of Green functions with large number of external legs. It is shown that the truncated equation for the two-photon-two-fermion vertex reproduces the lowest-order perturbative result in the limit of the small coupling constant. Furthermore, this equation allows to define an iterative procedure to compute higher order corrections in the coupling constant. The Ward-Takahashi identity for the two-photon-two-fermion irreducible vertex is derived and solved in the soft photon limit, where one of the photon momenta vanish, in the low photon momenta limit and for general kinematics. The solution of the Ward-Takahashi identity determines the longitudinal component of the two-photon-two-fermion irreducible vertex, while it is proposed to use the Dyson-Schwinger equation to determine the transverse part of this irreducible diagram. The two-photon-two-fermion DSE is solved in heavy fermion limit, considering a simplified version of the QED vertices. The contribution of this irreducible vertex to a low-energy effective photon-fermion vertex is discussed and the fermionic operators that are generated are computed in terms of the fermion propagator functions.

hep-ph↗

arXiv2020

Symmetry restoration and the gluon mass in the Landau gauge

We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.

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