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A quantum correction to the Brans-Dicke theory due to interactions among matter fields is calculated, resulting in violation of WEP, hence giving a constraint on the parameter \omega far more stringent than accepted so far. The tentative estimate gives the lower bounds \gsim 10^{6} and \gsim 10^{8} for the assumed force-range \gsim 1m and \gsim 1AU, respectively

INDUCED VIOLATION OF WEAK EQUIVALENCE PRINCIPLE IN THE BRANS-DICKE THEORY