SHORT-DISTANCE PROPERTIES FROM LARGE DISTANCE BEHAVIOR

For slowly varying fields the vacuum functional of a quantum field the ory may be expanded in terms of local functionals. This expansion sati sfies its own form of the Schrodinger equation from which the expansio n coefficients can be found. For scalar field theory in 1 + 1 dimensio ns we show that this approach correctly reproduces the short-distance properties as contained in the counterterms. We also describe an appro ximate simplification that occurs for the sine-Gordon and sinh-Gordon vacuum functionals.