A quantum energy inequality for a non-commutative QFT

A bstract We present a quantum energy inequality (QEI) for quantum field theories formulated in non-commutative spacetimes, extending fundamental energy constraints to this generalized geometric framework. By using operator-theoretic methods inspired by the positivity map of Waldmann et al. [1], we construct linear combinations of deformed operators that generalize the commutative spacetime techniques of Fewster et al., [2]. These non-commutative analogs enable us the derivation of a lower bound on the deformed averaged energy density, ensuring the stability of the underlying quantum field theory. This advancement appears to represent the first successful extension of quantum energy inequalities (QEIs) to non-commutative spacetime geometries based on current research literature.