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The perturbative and nonperturbative renormalisation of quark-antiquark operators in lattice QCD with two flavours of clover fermions is investigated within the research programme of the QCDSF collaboration. Operators with up to three…
A momentum dependent quark mass may be incorporated into a quark model in a manner consistent with dynamically broken chiral symmetry. We use this to study the high $Q^2$ behavior of the vector, axialvector, scalar and pseudoscalar…
Using stochastic quantization method we derive gauge-invariant equations, connecting multilocal vacuum correlators of nonperturbative field configurations immersed into the quantum background. Three alternative methods of stochastic…
A new method for computing all elements of the lattice quark propagator is proposed. The method combines the spectral decomposition of the propagator, computing the lowest eigenmodes exactly, with noisy estimators which are 'diluted', i.e.…
This paper is concerned with an inverse source problem for the stochastic biharmonic operator wave equation. The driven source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical…
We compute fermionic observables relevant to the study of chiral symmetry in quenched QCD using the Overlap-Dirac operator for a wide range of the fermion mass. We use analytical results to disentangle the contribution from exact zero modes…
We consider the radial Dirac operator with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the…
We consider the 1D Dirac operator on the half-line with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties…
Perturbative estimates of operator coefficients for improved lattice actions are becoming increasingly important for precision simulations of many hadronic observables. Following previous work by Dimm, Lepage, and Mackenzie, we consider the…
We consider self-adjoint Dirac operators $\ham{D}=\ham{D}_0 + V(x)$, where $\ham{D}_0$ is the free three-dimensional Dirac operator and $V(x)$ is a smooth compactly supported Hermitian matrix. We define resonances of $\ham{D}$ as poles of…
We extend the recently proposed Time-Dependent Multi-Determinant approach (ref.[1]) to the description of fermionic propagators. The method hinges on equations of motions obtained using variational principles of Dirac type. In particular we…
Applying domain decomposition to the lattice Dirac operator and the associated quark propagator, we arrive at expressions which, with the proper insertion of random sources therein, can provide improvement to the estimation of the…
We describe a novel framework for partially quenched chiral perturbation theory based on the replica method. The computational rules are exceedingly simple. We illustrate these rules by computing the partially quenched chiral condensate to…
In this work we probe the QCD Anderson transition by studying spectral distributions of the massless overlap operator on gauge configurations created by the twisted mass at finite temperature collaboration (tmfT) with 2+1+1 flavors of…
We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and…
The quantum disc is used to define a noncommutative analogue of a dense coordinate chart and of left-invariant vector fields on quantum SU(2). This yields two twisted Dirac operators for different twists that are related by a gauge…
We present a nonparametric method for estimating the value and several derivatives of an unknown, sufficiently smooth real-valued function of real-valued arguments from a finite sample of points, where both the function arguments and the…
The Banks--Casher relation links the spontaneous breaking of chiral symmetry in QCD to the presence of a non-zero density of quark modes at the low end of the spectrum of the Dirac operator. Spectral observables like the number of modes in…
We determine the equation of state of QCD at finite chemical potential, to order $(\mu_B/T)^6$, for a system of 2+1 quark flavors. The simulations are performed at the physical mass for the light and strange quarks on several lattice…
This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an…