arXiv subjects

Nicolas Wink

Publications and source records attributed to Nicolas Wink.

29 records · Page 2Linked to original sources

arXiv2022

On Gauge Consistency In Gauge-Fixed Yang-Mills Theory

We investigate BRST invariance in Landau gauge Yang-Mills theory with functional methods. To that end, we solve the coupled system of functional renormalisation group equations for the momentum-dependent ghost and gluon propagator, ghost-gluon, and three- and four-gluon vertex dressings. The equations for both, transverse and longitudinal correlation functions are solved self-consistently: all correlation functions are fed back into the loops. Additionally, we also use the Slavnov-Taylor identities for computing the longitudinal correlation functions on the basis of the above results. Then, the gauge consistency of the solutions is checked by comparing the respective longitudinal correlation functions. We find good agreement of these results, hinting at the gauge consistency of our setup.

hep-th↗

arXiv2022

Local Discontinuous Galerkin for the Functional Renormalisation Group

We apply the Local Discontinuous Galerkin discretisation to flow equations of the O(N)-model in the Local Potential Approximation. The improved stability is directly observed by solving the flow equation for various $N$ and space-time dimensions $d$. A particular focus of this work is the numerical discretisation and its implementation. The code is publicly available, and is explained in detail here. It is realised as a module within the high performance PDE framework DUNE.

hep-th↗

arXiv2022

Reconstructing QCD Spectral Functions with Gaussian Processes

We reconstruct ghost and gluon spectral functions in 2+1 flavor QCD with Gaussian process regression. This framework allows us to largely suppress spurious oscillations and other common reconstruction artifacts by specifying generic magnitude and length scale parameters in the kernel function. The Euclidean propagator data are taken from lattice simulations with domain wall fermions at the physical point. For the infrared and ultraviolet extensions of the lattice propagators as well as the low-frequency asymptotics of the ghost spectral function, we utilize results from functional computations in Yang-Mills theory and QCD. This further reduces the systematic error significantly. Our numerical results are compared against a direct real-time functional computation of the ghost and an earlier reconstruction of the gluon in Yang-Mills theory. The systematic approach presented in this work offers a promising route towards unveiling real-time properties of QCD.

hep-ph↗

arXiv2022

QMeS-Derivation: Mathematica package for the symbolic derivation of functional equations

We present the Mathematica package QMeS-Derivation. It derives symbolic functional equations from a given master equation. The latter include functional renormalisation group equations, Dyson-Schwinger equations, Slavnov-Taylor and Ward identities and their modifications in the presence of momentum cutoffs. The modules allow to derive the functional equations, take functional derivatives, trace over field space, apply a given truncation scheme, and do momentum routings while keeping track of prefactors and signs that arise from fermionic commutation relations. The package furthermore contains an installer as well as Mathematica notebooks with showcase examples.

hep-ph↗

arXiv2021

Ghost spectral function from the spectral Dyson-Schwinger equation

We compute the ghost spectral function in Yang-Mills theory by solving the corresponding Dyson-Schwinger equation for a given input gluon spectral function. The results encompass both scaling and decoupling solutions for the gluon propagator input. The resulting ghost spectral function displays a particle peak at vanishing momentum and a negative scattering spectrum, whose infrared and ultraviolet tails are obtained analytically. The ghost dressing function is computed in the entire complex plane, and its salient features are identified and discussed.

hep-th↗

arXiv2021

Shocks and quark-meson scatterings at large density

We discuss the phase structure of the two-flavour quark-meson model including quantum, thermal, density and critical fluctuations with the functional renormalisation group. This study combines two technical advances in the literature, that are also chiefly important for the quantitative access of the phase boundary of QCD at large density or baryon chemical potential. Specifically we allow for the formation and propagation of shocks as well as a fully self-consistent computation of the order parameter potential for chiral symmetry breaking.

hep-ph↗

arXiv2021

Spectral Reconstruction with Deep Neural Networks

We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem. Our ansatz is based on a supervised learning framework in which prior knowledge is encoded in the training data and the inverse transformation manifold is explicitly parametrised through a neural network. We systematically investigate this novel reconstruction approach, providing a detailed analysis of its performance on physically motivated mock data, and compare it to established methods of Bayesian inference. The reconstruction accuracy is found to be at least comparable, and potentially superior in particular at larger noise levels. We argue that the use of labelled training data in a supervised setting and the freedom in defining an optimisation objective are inherent advantages of the present approach and may lead to significant improvements over state-of-the-art methods in the future. Potential directions for further research are discussed in detail.

physics.comp-ph↗

arXiv2020

Spectral functions in the $ϕ^4$-theory from the spectral DSE

We develop a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularisation. Therefore, the non-perturbative spectral renormalisation setup here respects all symmetries of the theories at hand. In particular this includes space-time symmetries as well as internal symmetries such as chiral symmetry, and gauge symmetries. Spectral renormalisation can be applied within general functional approaches such as the functional renormalisation group, Dyson-Schwinger equations, and two- or $n$-particle irreducible approaches. As an application we compute the full, non-perturbative, spectral function of the scalar field in the $ϕ^4$-theory in $2+1$ dimensions from spectral Dyson-Schwinger equations. We also compute the $s$-channel spectral function of the full $ϕ^4$-vertex in this theory.

hep-th↗

arXiv2018

Bound state properties from the Functional Renormalisation Group

We discuss an approach for accessing bound state properties, like mass and decay width, of a theory within the functional renormalisation group approach. An important cornerstone is the dynamical hadronization technique for resonant interaction channels. The general framework is exemplified and put to work within the two-flavour quark-meson model. This model provides a low-energy description of the dynamics of two-flavour QCD with quark and hadronic degrees of freedom. We compare explicitly the respective results for correlation functions and observables with first principle QCD results in a quantitative manner. This allows us to estimate the validity range of low energy effective models. We also present first results for pole masses and decay widths. Next steps involving real-time formulations of the functional renormalisation group are discussed.

hep-ph↗

arXiv2018

Reconstructing the gluon

We reconstruct the gluon spectral function in Landau gauge QCD from numerical data for the gluon propagator. The reconstruction relies on two novel ingredients: Firstly we derive analytically the low frequency asymptotics of the spectral function. Secondly we construct a functional basis from a careful consideration of the analytic properties of the gluon propagator in Landau gauge. This allows us to reliably capture the non-perturbative regime of the gluon spectrum. We also compare different reconstruction methods and discuss the respective systematic errors.

hep-ph↗

arXiv2017

Finite temperature spectral functions in the O(N)-model

We directly calculate spectral functions in the O(N)-model at finite temperature within the framework of the Functional Renormalization group. Special emphasis is put on a fully numerical framework involving four-dimensional regulators preserving Euclidean O(4) and Minkowski Lorentz invariance, an important prerequisite for future applications. Pion and sigma meson spectral functions are calculated for a wide range of temperatures across the phase transition illustrating the applicability of the general framework for finite temperature applications. In addition, various aspects concerning the interplay between the Euclidean and real time two-point function are discussed.

hep-th↗