Generalized free field-like U(1)-Gauge theories within the wightman framework

Generalized free field-like U(1)-gauge theories are considered as an application of the Wightman theory to some special gauge field theories within the Borchers-Uhlmann approach to general QFT (without linear program). Along these lines, conditions upon the pseudo-Wightman functional are given such that the reconstructed indefinite-metric space D of state vectors decomposes into the direct sum of charge sectors labelled by the elements of the Pontrjagin dual group of a compact and Abelian gauge group G. ese gauge groups G are characterized in such a way that the positive definiteness of states of the vacuum sector holds. Furthermore, observable fields not carrying any charges as well as charge carrying fields are given. Finally, an example covering charged scalar free fields of mass m > 0 is discussed within that context.