J. Loeffelholz, G. Morchio, F. Strocchi
Ground state and functional integral representations of the CCR
algebra with free evolution
(51K, LaTeX 2e)
ABSTRACT. The ground state representations on the CCR algebra with free
evolution are classified and shown to be either non regular or
indefinite. In both cases one meets mathematical structures which
appear as prototypes of phenomena typical of gauge quantum field
theory. The functional integral representation in the positive non
egular case is discussed in terms of a generalized stochastic
process satisfying the Markov property. In the indefinite case the
ground state is faithful and its GNS representation is
characterized in terms of a KMS operator. In the corresponding
euclidean formulation, one has a generalization of the
Osterwalder-Schrader reconstruction and the indefinite Nelson
space, defined by the Schwinger functions, has a unique Krein
structure allowing for the construction of Nelson projections,
which satisfy the Markov property. The Schwinger functions can be
represented in terms of a functional measure and complex
variables.