Quantum Measurements of Space-Time Events

The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube is endowed with a natural positive-definite Riemannian metric that fully accommodates the geometry of the indefinite Minkowski space-time metric, together with its symmetries. These structures are sufficiently rich to allow one to construct a quantum theory of phase-space events, hence offering a way around the impasse of the particle paradigm of quantum field theory. In particular, a consistent theory of quantum measurement can be formulated in a relativistic setting, based on the use of positive operator valued measures, hence allowing one to assign probabilities to the outcomes of joint space-time and four-momentum measurements in a manifestly covariant framework.