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We develop a dynamical symmetry approach to path integrals for generalinteracting quantum spin systems. The time-ordered exponential obtained afterthe Hubbard-Stratonovich transformation can be disentangled into the product ofa finite number of the usual exponentials. This procedure leads to a set ofstochastic differential equations on the group manifold, which can be furtherformulated in terms of the supersymmetric effective action. This action has theform of the Witten topological field theory in the continuum limit. As aconsequence, we show how it can be used to obtain the exact results for aspecific quantum many-body system which can be otherwise solved only by theBethe ansatz. To our knowledge this represents the first example of a many-bodysystem treated exactly using the path integral formulation. Moreover, ourmethod can deal with time-dependent parameters, which we demonstrateexplicitly.

Dynamical symmetry approach and topological field theory for path integrals of quantum spin systems