Abstract
A definition of a Markov field is given which allows for noncommuting fields. In the commutative case, we recover Nelson's definition ( E. Nelson, Construction of quantum fields from Markoff fields, J. Functional Analysis 12 (1973) , 97–112). Conditional expectations are shown to exist in a regular probability gage space, and, using an independence property of these in the free fermion gage space, it is shown that the free fermion field over H −1( R d ) is a Markov field.
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