Two unique works about BRST cohomology [2] [3] miraculously inspire me to rewrite [1]. In the old preprint [1] we were thrown into confusion of gauge dependence about the Schwinger model with strong coupling limit, though in a very intelligible work [4] the authors concluded that the correlation functions of physical operators are constant. To put it differently they do not depend on any local coordinates. It is the property of the topological field theory. From a mathmatical proof which is connected with the gauge invariance of the energy-momentum tensors, we know that the energy-momentum tensor of the Yang-Mills theory can be always redefined so as to be BRST invariant [3]. Hence the present author optimistically decide to expect that under any gauge fixing conditions the Schwinger model with strong coupling limit is a topological field theory since the energy-momentum tensors can be always improved as a BRST invariant one and since we have shown that the energy-momentum tensors under two kinds of gauges can be represented as a commutator [Q_<BRST>, X], namely δ_BX [I]. Here δ_B denotes the BRST transformation.
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