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Excerpt from Euclidean Quantum Field Theory I: Equations for a Scalar Model
Eqft is of no particular interest in an axiomatic framework since the axioms are formulated directly in mqft terms and all of eqft is secondary. If, however, a Lagrangian is given, the situation is quite different. Then the investigation of the resulting particular system of integral equations for eqpt Green's functions becomes useful since the existence of a solution is a necessary condition for a corresponding mqft to exist, provided one supposes the mqft to possess a lowest - energy state as is done generally, and may be easier to prove or disprove.
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