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Jeroen C. Vink

Publications and source records attributed to Jeroen C. Vink.

17 recordsLinked to original sources
arXiv2022

Quantum Equilibrium in Stochastic de Broglie-Bohm-Bell Quantum Mechanics

This paper investigates dynamical relaxation to quantum equilibrium in the stochastic de Broglie-Bohm-Bell formulation of quantum mechanics. The time-dependent probability distributions are computed as in a Markov process with slowly varying transition matrices. Numerical simulations, supported by exact results for the large-time behavior of sequences of (slowly varying) transition matrices, confirm previous findings that indicate that de Broglie-Bohm-Bell dynamics allows an arbitrary initial probability distribution to relax to quantum equilibrium; i.e., there is no need to make the ad-hoc assumption that the initial distribution of particle locations has to be identical to the initial probability distribution prescribed by the system's initial wave function. The results presented in this paper moreover suggest that the intrinsically stochastic nature of Bell's formulation, which is arguable most naturally formulated on an underlying discrete space-time, is sufficient to ensure dynamical relaxation to quantum equilibrium for a large class of quantum systems without the need to introduce coarse-graining or any other modification in the formulation.

quant-ph↗
arXiv2022

Spin and Contextuality in Extended de Broglie-Bohm-Bell Quantum Mechanics

This paper introduces an extension of the de Broglie-Bohm-Bell formulation of quantum mechanics, which includes intrinsic particle degrees of freedom, such as spin, as elements of reality. To evade constraints from the Kochen-Specker theorem the discrete spin values refer to a specific basis -- i.e., a single spin vector orientation for each particle; these spin orientations are, however, not predetermined, but dynamic and guided by the (reduced, spin-only) wave function of the system, which is conditional on the realized location values of the particles. In this way, the unavoidable contextuality of spin is provided by the wave function and its realized particle configuration, whereas spin is still expressed as a local property of the individual particles. This formulation, which furthermore features a rigorous discrete-time stochastic dynamics, allows for numerical simulations of particle systems with entangled spin, such as Bohm's version of the EPR experiment.

quant-ph↗
arXiv2017

Particle Trajectories for Quantum Field Theory

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic Quantum Field Theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm's approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic Quantum Field Theory. In the present paper, Bell's formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of (stochastic) trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model.

quant-ph↗
arXiv2015

Stochastic Quantum Trajectories without a Wave Function

After summarizing three versions of trajectory-based quantum mechanics, it is argued that only the original formulation due to Bohm, which uses the Schrödinger wave function to guide the particles, can be readily extended to particles with spin. To extend the two wave function-free formulations, it is argued that necessarily particle trajectories not only determine location, but also spin. Since spin values are discrete, it is natural to revert to a variation of Bohm's pilot wave formulation due originally to Bell. It is shown that within this formulation with stochastic quantum trajectories, a wave function free formulation can be obtained.

quant-ph↗
arXiv1994

Investigation of Laplacian Gauge Fixing for U(1) and SU(2) Gauge Fields

The Laplacian gauge on the lattice is investigated numerically using U(1) and SU(2) gauge fields. The problem of Gribov ambiguities is addressed and to asses the smoothness of the gauge fixed configurations, they are compared to configurations fixed to the Landau gauge. The results of these comparisons with the Landau gauge indicate that Laplacian gauge fixing works very well in practice and offers a viable alternative to Landau gauge fixing.

hep-lat↗
arXiv1994

Failure of the Regge approach in two dimensional quantum gravity

Regge's method for regularizing euclidean quantum gravity is applied to two dimensional gravity. We use two different strategies to simulate the Regge path integral at a fixed value of the total area: A standard Metropolis simulation combined with a histogramming method and a direct simulation using a Hybrid Monte Carlo algorithm. Using topologies with genus zero and two and a scale invariant integration measure, we show that the Regge method does not reproduce the value of the string susceptibility of the continuum model. We show that the string susceptibility depends strongly on the choice of the measure in the path integral. We argue that the failure of the Regge approach is due to spurious contributions of reparametrization degrees of freedom to the path integral.

hep-lat↗
arXiv1993

Making chiral fermion actions (almost) gauge invariant using Laplacian gauge fixing

Straight foreward lattice descriptions of chiral fermions lead to actions that break gauge invariance. I describe a method to make such actions gauge invariant (up to global gauge transformations) with the aid of gauge fixing. To make this prescription unambiguous, Laplacian gauge fixing is used, which is free from Gribov ambiguities.

hep-lat↗
arXiv1993

Chiral gauge theories on the lattice and restoration of gauge symmetry

We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. We aim at a dynamical restoration of the gauge invariance in the full quantum model. If the gauge symmetry breaking (SB) is not too severe, this procedure could lead in the continuum limit to the desired gauge invariant chiral gauge theory.

hep-lat↗
arXiv1993

Almost Gauge Invariant Lattice Actions for Chiral Gauge Theories, using Laplacian Gauge Fixing

It is described how to obtain an almost gauge invariant lattice action $S$ for chiral gauge theories, or other models in which a straightforward discretization leads to a lattice action $S^\pr$ in which gauge invariance is broken. The lattice action is `almost' gauge invariant, because a local gauge transformation leaves the action the same, up to a global gauge transformation. In this approach the action $S$ for all gauge fields on a gauge orbit is the same as that of the action $S^\pr$ evaluated for the gauge field fixed to a smooth gauge. To define $S$ unambiguously, it must be possible to compute the gauge fixed field unambiguously. This rules out gauge conditions which suffer from Gribov ambiguities but it can be achieved by using the recently proposed Laplacian gauge. When using the almost gauge invariant action $S$ in a numerical simulation, it is not necessary to fix the gauge, and hence gauge fixing terms and Fadeev-Popov ghosts are not required. A hybrid Monte Carlo algorithm for simulations with this new action is described and tested on a simple toy model.

hep-lat↗
arXiv1993

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. ---- Note: 9 Postscript figures are appended as uuencoded compressed tar file.

hep-lat↗
arXiv1993

Non-gauge fixing approach to chiral gauge theories using staggered fermions

We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. Motivated by previous results in the non-gauge invariant massive Yang-Mills theory and certain gauge-fermion models we aim at a dynamical restoration of the gauge invariance in the full quantum model. If the gauge symmetry breaking is not too severe, this procedure could lead in the continuum limit to the desired gauge invariant chiral gauge theory. This scenario is very attractive since it does not rely on gauge fixing. We investigate a simple realization of this approach in a U(1) axial-vector model with dynamical fermions in four dimensions.

hep-lat↗
arXiv1993

Staggered fermions for chiral gauge theories: Test on a two-dimensional axial-vector model

As a first step towards constructing chiral models on the lattice with staggered fermions, we study a U(1) model with axial-vector coupling to an external gauge field in two dimensions. In our approach gauge invariance is broken, but it is restored in the classical continuum limit. We find that the continuum divergence relations for the vector and axial-vector currents are reproduced, up to contact terms, which we determine analytically. The current divergence relations are also studied numerically for smooth external gauge fields with topological charge zero. We furthermore investigate the effect of fluctuating gauge transformations and of gauge configurations with non-trivial topological charge.

hep-lat↗
arXiv1992

Can the Couplings in the Fermion-Higgs Sector of the Standard Model be Strong?

We present results for the renormalized quartic self-coupling $λ_R$ and the Yukawa coupling $y_R$ in a lattice fermion-Higgs model with two SU(2)$_L$ doublets, mostly for large values of the bare couplings. One-component (`reduced') staggered fermions are used in a numerical simulation with the Hybrid Monte Carlo algorithm. The fermion and Higgs masses and the renormalized scalar field expectation value are computed on $L^3 24$ lattices, where $L$ ranges from $6$ to $16$. In the scaling region these quantities are found to have a $1/L^2$ dependence, which is used to determine their values in the infinite volume limit. We then calculate the $y_R$ and $λ_R$ from their tree level definitions in terms of the masses and renormalized scalar field expectation value, extrapolated to infinite volume. The scalar field propagators can be described for momenta up to the cut-off by one fermion loop renormalized perturbation theory and the results for $λ_R$ and $y_R$ come out to be close to the tree level unitarity bounds. There are no signs that are in contradiction with the triviality of the Yukawa and quartic self-coupling.

hep-lat↗
arXiv1992

Fermion-Higgs model with Reduced Staggered Fermions

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 {\em 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 $16^3 24$.

hep-lat↗
arXiv1992

Gauge Fixing on the Lattice without Ambiguity

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.

hep-lat↗