Abstract

I will present an overview of possible extensions of the de Broglie-Bohm pilot-wave theory to quantum field theory. In such approaches, systems are not only described by their wave function, as in standard quantum theory, but also by some additional variables. In the non-relativistic pilot-wave theory of de Broglie and Bohm these variables are particle positions. In the context of quantum field theory, a number of approaches seem possible. I will discuss approaches with particle positions and with field configurations as additional variables. I will also consider the status of Lorentz invariance in these models. While they are Lorentz invariant at the empirical level (in quantum equilibrium), Lorentz invariance is violated at the fundamental level. I will present a way to achieve Lorentz invariance also at the fundamental level.