Evolution kernel for the dirac field

The evolution kernel for the free Dirac field is calculated using Wilson lattice fermions. We discuss the difficulties due to which this calculation has not been previously performed in continuum theory. The continuum limit is taken, and the complete energy eigenfunctions as well as the propagator are then evaluated in a new manner using the kernel.     

Variational estimates of chiral order parameter in 1+1 dimensional lattice QCD

We discuss analytically the vacuum structure and chiral-symmetry breaking in 1+1 dimensional lattice QCD with naive and Wilson fermions, using a unitary transformation and the variational method developed recently. As an example, the chiral order parameter is evaluated systematically for any coupling constant and fermion mass by including the multilink-terms in the transformation. The expected scaling behavior is observed. Our results are consistent with the continuum predictions.     

Stochastic models for lattice gauge theories

Stochastic equations are derived which describe the (Euclidean) time evolution of lattice field configurations, with and without fermions, on a three-dimensional space lattice. It is indicated how the drifts and transition functions may be obtained as asymptotic solutions of a differential equation or from a ground state ansatz. For non-Abelian gauge fields (without fermions) a ground state is constructed which is an exact eigenstate of a Hamiltonian with the same (naive) continuum limit as the Kogut-Susskind Hamiltonian. It is described how Euclidean correlations (like the Wilson loop) are obtained from the stochastic equations and how mass gaps may be obtained from the technique of exit times.     

Lattice fermions at non-zero temperature and chemical potential

We study the free fermion gas at finite temperature and chemical potential in the lattice regularized version proposed by Hasenfratz and Karsch and by Kogut et al. Special emphasis is placed on the identification of the particle and antiparticle contributions to the partition function. In the case of naive fermions we show that the partition function no longer separates into particle-antiparticle contributions in the way familiar from the continuum formulation. The use of Wilson fermions, on the other hand, eliminates this unpleasant feature, and leads, after subtracting the vacuum contributions, to the familiar expressions for the average energy and charge densities.     

QCD on the lattice and light hadron spectroscopy

Results in lattice Quantum Chromodynamics with fermions are reviewed. Estimates for the hadron spectrum on large lattices without and with light fermion polarization loops are discussed, and the results for different fermion regularizations are compared. The effects of the loops are found to be significant in lattice units, but to a greater part they can be reabsorbed in a redefinition of the overall scale. New estimates for the light quark masses with Wilson fermions are also presented. They differ substantially from previous estimates obtained by other methods in the continuum, and are much smaller. Finally it is argued that staggered fermions can lead to some anomalous results, which arise because of the doubling problem.     

IMPROVEMENT OF THERMODYNAMICAL MONTE CARLO SIMULATION IN SU(2) PURE GAUGE FIELD THEORY ——AN APPROACH TO CONTINUUM PHYSICS LIMIT

The thermodynamical quantities of SU(2) pure lattice gauge field have been simulated first time on the asymmetric lattice (ξ>1).The finite size effect and continuum physics limits have also been studied.The results show that the use of asymmetric lattice is of benefit to calculate the thermodynamical quantities and study the behavior of continuum physics limits.In addition,it is explained that the efficiency of the whole Monte Carlo simulation and the calculation of heat capacity will be improved quite a lot by using bias sampling technique.     

Observations on the Wilson fermions in the ϵ regime

We make several observations concerning the low quark mass region with Wilson fermions and how this is connected with the ? regime in the continuum. A transition from tiny cutoff effects to rather large discretization errors would take place in general with Wilson fermions if we lower the quark mass at finite lattice spacing. We argue that these two regions exhibit rather different behaviours concerning the coupling between cutoff effects and zero-modes. We interpolate between these two regimes adding to the continuum ? regime formulae, in the spirit of the Symanzik expansion, the relevant operators parametrising the leading cutoff effects. We compute the partition function, the chiral condensate, scalar and pseudo-scalar correlation functions. The final formulae can be used to fit lattice data to extract physical low energy constants, and to estimate systematic uncertainties coming from discretization errors. Moreover they suggest ways on how to remove these cutoff effects, the core of which are captured by the continuum zero modes.     

Hopping-parameter expansion and the Schwinger model with Wilson fermions

The hopping-parameter expansion method is used to study the Euclidean lattice Schwinger model with Wilson fermions. The effect of virtual fermion loops is also analyzed. The relation between the \(\bar \psi \psi\) operators in the continuum and on the lattice is constructed. Our result shows satisfactory scaling behavior and reproduces well the exactly calculable value for the fermion condensate in the continuum.     

Chiral and conformal anomalies in lattice gauge theory

The continuum limit of the chiral and conformal (Weyl) Ward-Takahashi identities in the lattice Wilson action is studied. The Wilson term works for the chiral anomaly, but it gives rise to-15 times the conventional conformal anomaly for a smallr-parameter and a very sensitiver-dependence of the Λ-parameter. This shows that the strong symmetry breaking by the Wilson term by itself does not necessarily generate correct anomalies. In the lattice regularization the functional Jacobian factors becomec-numbers and do not contribute to anomalies, corresponding to the cut-off of short distance components; the naive continuum limit of lattice WT identities can thus behave differently from continuum ones. To reconstruct conventional identities from lattice relations, the lattice composite operators should be rewritten in terms of relevant continuum operators. In general, this identification of relevant operators is facilitated either by the procedure corresponding to Zimmermann's normal product algorithm or simply by the use of auxiliary regulators such as the dimensional regulator.     

Wilson fermions and axion electrodynamics in optical lattices

We show that ultracold Fermi gases in optical superlattices can be used as quantum simulators of relativistic lattice fermions in 3+1 dimensions. By exploiting laser-assisted tunneling, we find an analogue of the so-called naive Dirac fermions, and thus provide a realization of the fermion doubling problem. Moreover, we show how to implement Wilson fermions, and discuss how their mass can be inverted by tuning the laser intensities. In this regime, our atomic gas corresponds to a phase of matter where Maxwell electrodynamics is replaced by axion electrodynamics: a 3D topological insulator.     

Vector meson radiative decay in lattice QCD

The amplitude for radiative decay of vector mesons is calculated in quenched lattice quantum chromodynamics using the Wilson scheme for fermions. The calculated decay strengths are consistently smaller than experimentally measured values at all values of the quark mass.     

Chiral symmetry on the lattice with Wilson fermions

The chiral properties of the continuum limit of lattice QCD with Wilson fermions are studied. We show that a partially conserved axial current can be defined, satisfying the usual current algebra requirements.A proper definition of the chiral symmetry order parameter, $\text{〈0|}\text{ψ}\text{ψ|0〉}$, is given, and the chiral properties of composite operators are investigated. The implications of our analysis to the lattice determination of non-leptonic weak amplitudes are also discussed.     

Non-perturbative renormalization of lattice four-fermion operators without power subtractions

A general nonperturbative analysis of the renormalization properties of four-fermion operators in the framework of lattice regularization with Wilson fermions is presented. We discuss the nonperturbative determination of the operator renormalization constants in the lattice regularization independent (RI or MOM) scheme. We also discuss the determination of the finite lattice subtraction coefficients from Ward identities. We prove that, at large external virtualities, the determination of the lattice mixing coefficients, obtained using the RI renormalization scheme, is equivalent to that based on Ward identities, in the continuum and chiral limits. As a feasibility study of our method, we compute the mixing matrix at several renormalization scales, for three values of the lattice coupling , using the Wilson and tree-level improved SW-Clover actions. Received: 26 February 1999 / Published online: 15 July 1999     

Simulating the all-order hopping expansion II: Wilson fermions

We investigate the extension of the Prokof'ev–Svistunov worm algorithm to Wilson lattice fermions in an external scalar field. We effectively simulate by Monte Carlo the graphs contributing to the hopping expansion of the two-point function on a finite lattice to arbitrary order. Tests are conducted for a constant background field i.e. free fermions at some mass. For the method introduced here this is expected to be a representative case. Its advantage is that we know the exact answers and can thus make stringent tests on the numerics. The approach is formulated in both two and three space–time dimensions. In D=2$D=2$ Wilson fermions enjoy special positivity properties and the simulation is similarly efficient as in the Ising model. In D=3$D=3$ the method also works at sufficiently large mass, but there is a hard sign problem in the present formulation hindering us to take the continuum limit.     

Fermions in a single-point model of QCD with many colours and flavours

I consider the fermion dynamics of a reduced model of Chromodynamics in the topological limit. Contrary to the lattice theory (with naive fermions) the reduced model has the same chiral symmetry as the continuum theory. The origin of the (perhaps benificial) error in the reduction procedure is discussed. Also I look for other reduced models.     

Λ-parameters for asymmetric lattice gauge theories with fermions

Dimensional quantities obtained from Monte Carlo simulations on the lattice depend on the lattice mass parameter, Λ_L. To make a connection with continuum physics, a relationship is needed between Λ_L and the Λ-parameters of the continuum theory. This has been done for the euclidean symmetric lattice by others. However, in order to incorporate finite temperature into Monte Carlo studies, or to study the transition from the euclidean formulation to the hamiltonian formulation of gauge theories, asymmetric lattices (a_s≠a_t) may be used. In this paper, the assymetric calculations are extended and the ratio $\text{Λ}{}_{\mathrm{<mtext>min</mtext>}}\text{Λ}{}_{\mathrm{<mtext>L</mtext>}}$, where Λ_min is the continuum mass parameter in the minimal subtraction scheme, is given to one loop for n_f flavors of Wilson and Susskind massless fermions on an asymmetric four-dimensional lattice for two different asymmetric lattice actions.     

Overlap valence quarks on a twisted mass sea: A case study for mixed action lattice QCD

We discuss a lattice QCD mixed action investigation employing Wilson maximally twisted mass sea and overlap valence fermions. Using four values of the lattice spacing, we demonstrate that the overlap Dirac operator assumes a point-like locality in the continuum limit. We also show that by adopting suitable matching conditions for the sea and valence theories a consistent continuum limit for the pion decay constant and light baryon masses can be obtained. Finally, we confront results for sea–valence mixed meson masses and the valence scalar correlator with corresponding expressions of chiral perturbation theory. This allows us to extract low energy constants of mixed action chiral perturbation which characterize the strength of unitarity violations in our mixed action setup.     

The phase structure of lattice QCD with two flavors of Wilson quarks and renormalization group improved gluons

The effect of changing the lattice action for the gluon field on the recently observed [F. Farchioni, R. Frezzotti, K. Jansen, I. Montvay, G.C. Rossi, E. Scholz, A. Shindler, N. Ukita, C. Urbach, I. Wetzorke, Eur. Phys. J. C 39, 421 (2005); hep-lat/0406039] first order phase transition near zero quark mass is investigated by replacing the Wilson plaquette action by the DBW2 action. The lattice action for quarks is unchanged: it is in both cases the original Wilson action. It turns out that Wilson fermions with the DBW2 gauge action have a phase structure where the minimal pion mass and the jump of the average plaquette are decreased, when compared to Wilson fermions with Wilson plaquette action at similar values of the lattice spacing. Taking the DBW2 gauge action is advantageous also from the point of view of the computational costs of numerical simulations.Received: 29 October 2004, Revised: 7 March 2005, Published online: 31 May 2005