Relativistic resonances, relativistic Gamow vectors and representations of the Poincare semigroup

The foundations of time asymmetric quantum theory are reviewed and are applied to the construction of relativistic Gamow vectors. Relativistic Gamow vectors are obtained from the resonance pole of the S-matrix and furnish an irreducible representation of the Poincar´e semigroup. They have all the prop- erties needed to represent relativistic quasistable particles and can be used to fix the definition of mass and width of relativistic resonances like the Z-boson. Most remarkably, they have only a semigroup time evolution into the forward light cone—expressing time asymmetry on the microphysical level.