2025/03/31 by Grosse, Harald, Much, Albert · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2503.24068
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 leveraging operator-theoretic methods inspired by the positivity map of Waldmann et al. \citewaldmannpos, we construct linear combinations of deformed operators that generalize the commutative spacetime techniques of Fewster et al., \citeFew98. 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. Our result establishes rigorous constraints on the expectation values of the deformed (non-commutative) energy density, reinforcing the physical consistency of non-commutative models while preserving core principles of quantum field theory.