ℱ(P) quantum mechanics

Abstract

We explore the possibility to extend the Heisenberg’s uncertainty principle to a nonlinear extension of the quantum algebra related to a functional operator of the momenta as [Formula: see text]. We show that such an extension of quantum mechanics is intimately connected to the non-commutative space-time algebra and the Lorentz symmetry deformations. We show that a large class of [Formula: see text] models can introduce superluminal modes in the quantized theories. We also show that the Hořava–Lifshitz theory is related to a large class of [Formula: see text] Quantum Mechanics.