Yang-Mills beta-function from a large-distance expansion of the Schrodinger functional

For slowly varying fields the Yang-Mills Schrodinger functional can be expa nded in terms of local functionals. We show how analyticity in a complex sc ale parameter enables the Schrodinger functional for arbitrarily varying fi elds to be reconstructed from this expansion. We also construct the form of the Schrodinger equation that determines the coefficients. Solving this in powers of the coupling reproduces the results of the 'standard' perturbati ve solution of the functional Schrodinger equation which we also describe. In particular the usual result for the beta-function is obtained illustrati ng how analyticity enables the effects of rapidly varying fields to be comp uted from the behaviour of slowly varying ones. (C) 1999 Elsevier Science B .V.