Jeroen C. Vink

Remnants of the Index Theorem on the Lattice

Abstract We investigate the spectrum of lattice Dirac operators in two dimensions in external U(1) gauge fields as well as the properties and renormalization of the quantity m Tr γ 5 /(¶ + m) which provides a definition of topological charge based on axial-vector divergence relations.

Renormalized Ward-Takahashi relations and topological susceptibility with staggered fermions

Abstract Local (axial) vector currents and (pseudo) scalar fields are constructed, renormalized and used to derive Ward-Takahashi relations for staggered fermions in lattice QCD. With the help of these a lattice derivation is given of the Witten-Veneziano formula for the flavor singlet pseudoscalar particle. We discuss how the ensuing topological susceptibility is to be evaluated and argue that it is finite.

Gauge fixing on the lattice without ambiguity

Abstract A new gauge fixing condition is discussed, which is (lattice) rotation invariant, has the “smoothness” properties of the Landau gauge but can be efficiently computed and is unambiguous for almost all lattice gauge field configurations.

Staggered fermions and topological susceptibility in lattice QCD at β = 5.7

Abstract In this pilot study we use staggered fermions to estimate the topological susceptibility of SU(3) lattice gauge theory at β = 5.7.

Neutral Pseudoscalar Masses in Lattice {QCD}

Abstract A lattice derivation is given of the Witten-Veneziano mass formulas for the neutral pseudoscalar bosons.

Quantum potential interpretation of the wave function of the universe

Abstract The quantum potential interpretation of quantum mechanics due to Bohm is applied to the Wheeler-De Witt equation for minisuperspace.

Investigation of the domain wall fermion approach to chiral gauge theories on the lattice

We investigate a recent proposal to construct chiral gauge theories on the lattice using domain wall fermions. We restrict ourselves to the finite volume case, in which two domain walls are present, with modes of opposite chirality on each of them. We couple the chiral fermions on only one of the domain walls to a gauge field. In order to preserve gauge invariance, we have to add a scalar field, which gives rise to additional light mirror fermion and scalar modes. We argue that in an anomaly-free model these extra modes would decouple if our model possesses a so-called strong coupling symmetric phase. However, our numerical results indicate that such a phase most probably does not exist.

Thermalization in a Hartree ensemble approximation to quantum field dynamics

For homogeneous initial conditions, Hartree (gaussian) dynamical approximations are known to have problems with thermalization, because of insufficient scattering. We attempt to improve on this by writing an arbitrary density matrix as a superposition of gaussian pure states and applying the Hartree approximation to each member of such an ensemble. Particles can then scatter via their back-reaction on the typically inhomogeneous mean fields. Starting from initial states which are far from equilibrium we numerically compute the time evolution of particle distribution functions and observe that they indeed display approximate thermalization on intermediate time scales by approaching a Bose-Einstein form. However, for very large times the distributions drift towards classical-like equipartition.

Fermion-Higgs model with reduced staggered fermions

Abstract We introduce a lattice fermion-Higgs model with one component ‘reduced staggered’ fermions. In order to use the fermion field as efficiently as possible we couple the two staggered flavors to the O(4) Higgs field leading to a model with only one SU(2) doublet in the scaling region. The number of fermions is doubled in a numerical investigation of the model with the hybrid Monte Carlo algorithm. We present results for the phase diagram, particle masses and renormalized couplings on lattices ranging in size from 6 3 24 to 16 3 24.

Topological charge and fermions in the two-dimensional lattice U(1) model (I): Staggered fermions

Abstract We investigate various definitions of topological charge within the compact QED 2 model. In particular we study for staggered fermions the charge, Q = 1 2 ϰ P m Tr Γ 5 ( D + m) − and its renormalization factor ϰ P .