When considering path integrals with grassmann variables, as stated on page 159 of Quantization of gauge systems - Henneaux, Teitelboim we only have one boundary condition, since the equations of motion are first order. The following action is then introduced

$$ S = \int_{t_1}^{t_2} L \, dt - \frac{i}{2}\theta^i(t_1)\theta_i(t_2)$$

saying that "the solutions of the equations of motion are those histories that yeld no variations of $S$ under the conditions

$$ \delta (\theta(t_1)+\theta(t_2))=0. $$

What does this condition actually mean? Do the boundary conditions change when we consider a variation $\delta S$?


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