  A fully quantum version of the Witten-Olive analysis of the central charge in
the N=1 Wess-Zumino model in $d=2$ with a kink solution is presented by using
path integrals in superspace. We regulate the Jacobians with heat kernels in
superspace, and obtain all superconformal anomalies as one Jacobian factor. The
conserved quantum currents differ from the Noether currents by terms
proportional to field equations, and these terms contribute to the anomalies.
We identify the particular variation of the superfield which produces the
central charge current and its anomaly; it is the variation of the auxiliary
field. The quantum supersymmetry algebra which includes the contributions of
superconformal anomalies is derived by using the Bjorken-Johnson-Low method
instead of semi-classical Dirac brackets. We confirm earlier results that the
BPS bound remains saturated at the quantum level due to equal anomalies in the
energy and central charge.
