How To Fix Non-Perturbatively A Parameter Dependent Covariant Gauge On The Lattice

We describe how to overcome some problems that usually prevent from obtaining an efficient algorithm to fix a generic covariant gauge on the lattice. This gauge is the lattice equivalent of the generic gauge usually adopted in perturbative calculations. It depends on a parameter whose value can be varied in order to check the gauge dependence of measured matrix elements.Comment: 3 pages, 2 eps figures, LATTICE 9

Quark and Gluon Propagators in Covariant Gauges

We present data for the gluon and quark propagators computed in the standard lattice Landau's gauge and for three values of the covariant gauge-fixing parameter lambda=0,8,16. Our results are obtained using the SU(3) Wilson action in the quenched approximation at beta=6.0 and volume=16^3x32.Comment: Lattice2001(theorydevelop

Numerical Exploration of the RI/MOM Scheme Gauge Dependence

The gauge dependence of some fermion bilinear RI/MOM renormalization constants is studied by comparing data which have been gauge-fixed in two different realizations of the Landau gauge and in a generic covariant gauge. The very good agreement between the various sets of results and the theory indicates that the numerical uncertainty induced by the lattice gauge-fixing procedure is below the statistical errors of our data sample which is of the order of (1-1.5)%.Comment: 3 pages, 2 figures, Lattice2002(theoretical

On the Definition of Gauge Field Operators in Lattice Gauge-Fixed Theories

We address the problem of defining the gauge four-potential on the lattice, in terms of the natural link variables. Different regularized definitions are shown, through non perturbative numerical computation, to converge towards the same continuum renormalized limit.Comment: 8 pages, LaTeX2e/LaTeX209, 3 eps figure

Thermal field theories and shifted boundary conditions

The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: they offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedure.Comment: 7 pages, 1 figure, talk presented at the 31st International Symposium on Lattice Field Theory - Lattice 2013, Mainz, German

Relativistic descriptions of final-state interactions in neutral-current neutrino-nucleus scattering at MiniBooNE kinematics

The analysis of the recent neutral-current neutrino-nucleus scattering cross sections measured by the MiniBooNE Collaboration requires relativistic theoretical descriptions also accounting for the role of final state interactions. In this work we evaluate differential cross sections with the relativistic distorted-wave impulse-approximation and with the relativistic Green's function model to investigate the sensitivity to final state interactions. The role of the strange-quark content of the nucleon form factors is also discussed.Comment: 8 pages, 5 figure

Topological susceptibility in the SU(3) gauge theory

We compute the topological susceptibility for the SU(3) Yang--Mills theory by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi=(191 +/- 5 MeV)^4 if F_K is used to set the scale. Our result supports the Witten--Veneziano explanation for the large mass of the eta'.Comment: Final version to appear on Phys. Rev. Let

Remarks on the Gauge Dependence of the RI/MOM Renormalization Procedure

The RI/MOM non-perturbative renormalization scheme is studied on the lattice in SU(3) quenched QCD with Wilson fermions. The gauge dependence of some fermion bilinear renormalization constants is discussed by comparing data which have been gauge-fixed in two different realizations of the Landau gauge and in a generic covariant gauge. The very good agreement between the various sets of results and the theory indicates that the numerical uncertainty induced by the lattice gauge-fixing procedure is moderate and below the statistical errors.Comment: 11 pages, 3 figure

Polar Varieties and Efficient Real Elimination

Let $S_0$ be a smooth and compact real variety given by a reduced regular sequence of polynomials $f_1, ..., f_p$. This paper is devoted to the algorithmic problem of finding {\em efficiently} a representative point for each connected component of $S_0$ . For this purpose we exhibit explicit polynomial equations that describe the generic polar varieties of $S_0$. This leads to a procedure which solves our algorithmic problem in time that is polynomial in the (extrinsic) description length of the input equations $f_1, >..., f_p$ and in a suitably introduced, intrinsic geometric parameter, called the {\em degree} of the real interpretation of the given equation system $f_1, >..., f_p$.Comment: 32 page

Polar Varieties, Real Equation Solving and Data-Structures: The hypersurface case

In this paper we apply for the first time a new method for multivariate equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for complex root determination to the {\em real} case. Our main result concerns the problem of finding at least one representative point for each connected component of a real compact and smooth hypersurface. The basic algorithm of \cite{gh1}, \cite{gh2}, \cite{gh3} yields a new method for symbolically solving zero-dimensional polynomial equation systems over the complex numbers. One feature of central importance of this algorithm is the use of a problem--adapted data type represented by the data structures arithmetic network and straight-line program (arithmetic circuit). The algorithm finds the complex solutions of any affine zero-dimensional equation system in non-uniform sequential time that is {\em polynomial} in the length of the input (given in straight--line program representation) and an adequately defined {\em geometric degree of the equation system}. Replacing the notion of geometric degree of the given polynomial equation system by a suitably defined {\em real (or complex) degree} of certain polar varieties associated to the input equation of the real hypersurface under consideration, we are able to find for each connected component of the hypersurface a representative point (this point will be given in a suitable encoding). The input equation is supposed to be given by a straight-line program and the (sequential time) complexity of the algorithm is polynomial in the input length and the degree of the polar varieties mentioned above.Comment: Late