Explicit Observers

M.L.J. Hautus, René Boite, P. Dewilde

Maxine Pitter Lunn

An elementary proof of the results of Wightman concerning the existence and non-existence of position observables for relativistic systems is presented. The method uses an explicitly described unitary transformation to relate the representations of the Euclidean group obtained by restricting the m not=0 representations of the Poincare group to representions having position observables. The position observables are displayed explicitly as differential operators in the cases in which they exist.

Daniela Cadamuro

In quantum field theory, the rigorous construction of local observables in the presence of nontrivial interaction is a crucial problem. In a class of integrable quantum field theories, a very abstract existence proof has recently been given by Lechner. We give an explicit characterization of these local observables in terms of the properties of the coefficient functions in an expansion by interacting creators and annihilators. Some results on the operator domains of these local observables are given. Using these, we constructed explicit examples of local observables in the quantum Ising model.

Hector Dehesa

S. A. Gardiner, J. I. Cirac, P. Zoller

We describe a method to perform a single quantum measurement of an arbitrary motional observable of a single ion moving in a harmonic potential. We illustrate the measurement procedure with explicit examples, namely the position and phase observables. A necessary tool for this is the ability to synthesize an arbitrary motional state. In addition, we show how to generalize this to higher dimensions, and show explicit examples of how to engineer states in two spatial dimensions, including a proposed experimental configuration.

Daniel John Murray