Abstract
The infinite-dimensional Ornstein-Uhlenbeck process associated with the free field of quantum field theory on R d is reconstructed as the traces of random harmonic functions. These harmonic functions are the solutions of a generalised Dirichlet problem with a (random) Schwartz distribution as boundary data. A detailed analysis of the associated trace space, which is a subspace of a scaled Sobolev space of negative fractional order, leads to a new path space for the free field as well as to a convenient regularisation method. Because of the particular form of the trace space it is possible to give an explicit formula for the transition function of the process. Furthermore, the dependence of the path space on the dimension d is discussed and a formulation of our result in terms of abstract Wiener spaces is given.
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