Local formulations of QFT imply that gauge theory correlators can potentially contain generalised infrared poles. In this talk I will outline the theoretical significance of these components, and report on recent lattice fit results for the gluon propagator.
The inability to distinguish inertial coordinate systems by measuring
quantum observables implies that equivalent states in different
inertial coordinate systems are related by a unitary representation of
the Poincar\'e group on the Hilbert space of the quantum theory.
These representations can be decomposed into a direct integral of
irreducible representations. This decomposition is...
I discuss results of a recent study on the analytic structure of the quark propagator in Minkowski space. The analytic structure of the quark propagator in Minkowski space is more complex than in Euclidean space due to the possible existence of poles and branch cuts at timelike momenta. Here I discuss a computational method based on the spectral representation of the propagator. The method...
Given any effective Hamiltonian possessing the mechanism of spontaneous chiral symmetry it can be mapped to an equivalent problem of several interacting spins, by means of a Bravyi-Kitaev transformation. Jordan-Wigner transformations are also discussed.
The resulting Hamiltonian is on a suitable form to be implemented on a digital quantum computer, where spins are mapped into qubits. We...
I will present an overview of results for gluon, ghost and quark propagators and veretices from lattice QCD, and discuss what this may tell us about their analytic structure.
We study the continuum limit of SU(2) Landau-gauge gluon and ghost propagators, obtained from numerical simulations performed on lattice volumes of up to $192^4$, in the scaling region.
We report on the computation of the quark propagator at finite temperature in the Landau gauge using quenched gauge configurations. The propagator form factors are computed for various temperatures, above and below the gluon deconfinement temperature $T_c$, and for all the Matsubara frequencies. Significant differences are found between the form factores below and above $T_c$, which suggest a...
Dyson-Schwinger studies of the fermion propagator are typically performed in Euclidean metric, providing information on the nonperturbative behavior of the fermion propagator at spacelike momenta. It has been known for more than 40 years that an analytic continuation to the entire complex momentum plane can, and often does, reveal 'mass-like' singularities at complex-conjugate momenta, even...
The pion structure in Minkowski space is described in terms of an analytic model of the Bethe–Salpeter amplitude combined with Euclidean Lattice QCD results.
The model is physically motivated to take into account the running quark mass, which is fitted to Lattice QCD data. In the present work, we extend the an previus work, with the present model utilized to calculated the pion...
An important tool to deal with the formulation in Minkowski space is the Integral
Representation (IR) proposed by Nakanishi.
In this work, we use the IR to obtain a solution of the Dyson-Schwinger equation directly in Minkowski space, and compare with a solution in a rotated axis from the Euclidean axis, what we call ``Un-Wick rotation''. To this end we must find the relation between the...
We show results for propagators and vertices in Yang-Mills theory and QCD obtained from the 3PI effective action. Their use in calculating bound-states and resonances requires access to complex momenta, necessitating special care. We perform appropriate deformations of the integration contour to avoid cuts and poles and present corresponding results for bound states as well as first results...
A survey of the challenges in solving the ladder Bethe-Salpeter equation with spin dof, within an approach able to be played directly in Minokowski space, is presented. The interesting features of the light-front distributions for both two-fermion and fermion-scalar bound systems are discussed in view of possible correlations with the underlying dynamical interaction.
We shall report on the model building of the pion GPD, within the DGLAP kinematic region, through the overlap of light-front wave functions. The wave functions can be modelled on the basis of the so-called Nakanishi representation and brought to make contact with realistic solutions of the Bethe-Salpeter equation. Then, we will capitalise on a new type of process-independent QCD charge to...
The extraction of spectral functions from Euclidean correlator data, simulated non-perturbatively at finite temperature, using first principles lattice QCD is a central challenge of modern high energy nuclear physics. In this talk I will first discuss different theoretical approaches, currently deployed to attack this problem, before showcasing recent progress and outstanding challenges in the...
We calculate the onshell 2 → 2 scattering amplitude in a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations. The integrals produce branch cuts in the complex plane of the integrand which prohibit a naive Euclidean integration path. By employing contour deformations, we can also access the kinematical regions associated with the...
Heavy quarkonium has been solved as a relativistic bound state using Basis Light-Front Quantization (BLFQ), a non-perturbative Hamiltonian approach. We aim to extend the formalism from the valence Fock sector $|q \bar{q}>$ to higher Fock space by including the $|q \bar{q} q \bar{q}>$ sector, in hopes of bringing new aspects into the QCD bound states.
