01-233 J. Loeffelholz, G. Morchio, F. Strocchi

Ground state and functional integral representations of the CCR algebra with free evolution (51K, LaTeX 2e) Jun 29, 01

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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.

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