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Using the results of previous investigations on sine-Gordon form factorsexact expressions of all breather matrix elements are obtained for severaloperators: all powers of the fundamental bose field, general exponentials ofit, the energy momentum tensor and all higher currents. Formulae for theasymptotic behavior of bosonic form factors are presented which are motivatedby Weinberg's power counting theorem in perturbation theory. It is found thatthe quantum sine-Gordon field equation holds and an exact relation between the``bare'' mass and the renormalized mass is obtained. Also a quantum version ofa classical relation for the trace of the energy momentum is proven. Theeigenvalue problem for all higher conserved charges is solved. All results arecompared with perturbative Feynman graph expansions and full agreement isfound.Comment: LaTeX, 31 page

Sine-Gordon breather form factors and quantum field equations