Quadrangles embedded in metasymplectic spaces

During the final steps in the classification of the Moufang quadrangles by Jacques Tits and Richard Weiss a new class of Moufang quadrangles unexpectedly turned up. Subsequently Bernhard Muhlherr and Hendrik Van Maldeghem showed that this class arises as the fixed points and hyperlines of certain involutions of a metasymplectic space (or equivalently a building of type F_4). In the same paper they also showed that other types of Moufang quadrangles can be embedded in a metasymplectic space as points and hyperlines. In this paper, we reverse the question: given a (thick) quadrangle embedded in a metasymplectic space as points and hyperlines, when is such a quadrangle a Moufang quadrangle

Pilot-wave theory and quantum fields

Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector, but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schroedinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.Comment: 65 pages, no figures, LaTex; v2 minor changes, some extensions; v3 minor improvements; v4 some typos correcte

A new pilot-wave model for quantum field theory

We present a way to construct a pilot-wave model for quantum field theory. The idea is to introduce beables corresponding only to the bosonic degrees of freedom and not to the fermionic degrees of freedom of the quantum state. We illustrate this idea for quantum electrodynamics. The beables will be field beables corresponding to the electromagnetic field and they will be introduced in a similar way to that of Bohm's model for the free electromagnetic field. Our approach is analogous to the situation in non-relativistic quantum theory, where Bell treated spin not as a beable but only as a property of the wavefunction.Comment: 21 pages, no figures, LaTex, talk given at the conference "On the present status of quantum mechanics", 7-9 September, 2005, Mali Losinj, Croati

On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics

In Bohmian mechanics the distribution $|\psi|^2$ is regarded as the equilibrium distribution. We consider its uniqueness, finding that it is the unique equivariant distribution that is also a local functional of the wave function $\psi$.Comment: 15 pages, no figures, LaTe