RELATIVISTIC GAMOW VECTORS

The Friedrichs model has often been used in order to obtain explicit f ormulas for eigenvectors associated to complex eigenvalues correspondi ng to lifetimes. Such eigenvectors are called Gamow vectors and they a cquire meaning in extensions of the conventional Hilbert space of quan tum theory to the so-called rigged Hilbert space. In this paper, Gamow vectors are constructed for a solvable model of an unstable relativis tic field. As a result, we obtain a time asymmetric relativistic exten sion of the Fock space. This extension leads to two distinct Poincare semigroups. The time reversal transformation maps one semigroup to the other. As a result, the usual PCT invariance should be extended. We s how that irreversibility as expressed by dynamical semigroups is compa tible with the requirements of relativity. (C) 1998 American Institute of Physics.