Stochastic particle annihilation: a model of state reduction in relativistic quantum field theory

A model of state reduction in relativistic quantum field theory involving a nonlinear stochastic extension of Schr\"odinger's equation is outlined. The eigenstates of the annihilation operator are chosen as the preferred basis onto which reduction occurs. These are the coherent states which saturate the bound of the Heisenberg uncertainty relation, exhibiting classical-like behavior. The quantum harmonic oscillator is studied in detail before generalizing to relativistic scalar quantum field theory. The infinite rates of increase in energy density which have plagued recent relativistic proposals of dynamical state reduction are absent in this model. This is because the state evolution equation does not drive particle creation from the vacuum. The model requires the specification of a preferred sequence of space-like hyper-surfaces supporting the time-like state evolution. However, it is shown that the choice of preferred surfaces has no effect on perturbative results to second order in the coupling parameter. It is demonstrated how state reduction to a charge density basis can be induced in fermionic matter via an appropriate coupling to a bosonic field undergoing this mechanism.