Nonstandard methods in quantum field theory I: A hyperfinite formalism of scalar fields

摘要

A nonstandard approach to axiomatic quantum field theory is given. Nonstandard axioms for a Hermitian scalar field is proposed, where the field operators act on a hyperfinite-dimensional Hilbert space. The axioms are shown to be equivalent to the G (a) over circle rding-Wightman axioms. An example of a model of the nonstandard axioms is examined. [References: 20]