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The quasi-Poisson measures are considered, i.e., the σ-finite measures given by a density with respect to a Poisson measure. Representations of current groups are constructed in Hilbert spaces of functionals integrable with respect to a quasi-Poisson measure. For the groups O(n, 1) and U(n, 1), these models give new, more convenient, realizations of the representations in Fock spaces constructed in the previous papers by the authors. A crucial role in considerations is played by spaces of configurations and an analogy between quasi-Poisson and stable measures. §

The Poisson model of the Fock space and representations of current groups