Semiclassical energy conditions for quantum vacuum states

We present and develop several nonlinear energy conditions suitable for use in the semiclassical regime. In particular, we consider the recently formulated flux energy condition (FEC), and the novel trace-of-square (TOSEC) and determinant (DETEC) energy conditions. As we shall show, these nonlinear energy conditions behave much better than the classical linear energy conditions in the presence of semiclassical quantum effects. Moreover, whereas the quantum extensions of these nonlinear energy conditions seem to be quite widely satisfied as one enters the quantum realm, analogous quantum extensions are generally not useful for the linear classical energy conditions.