Abstract
A model of a field with bounded current density is investigated. It is shown that there exists an infinite-fold integral that determines a generating functional of the Schwinger functions. It is shown that this functional is the Fourier transform of a probability measure on the field trajectories that is concentrated in a Hilbert subspace of the space of tempered distributions of first order of singularity. It is shown that the field satisfies the strong regularity axiom of Osterwalder and Schrader.
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Additional information
Moscow Power Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 12–28, January, 1994.
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Kirillov, A.I. Field of sine-Gordon type in spacetime of arbitrary dimension: Existence of the nelson measure. Theor Math Phys 98, 8–19 (1994). https://doi.org/10.1007/BF01015118
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DOI: https://doi.org/10.1007/BF01015118