2021/03/07 by Sirous Homayouni, Homayouni, Sirous, Angelo B. Mingarelli +1
Mathematics · Physics and Astronomy · #46C20 #47B50 #81S07 #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2103.04372
openalex publication_date 2021/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Uncertainty relations between two general non-commuting self-adjoint operators are derived in a Krein space. All of these relations involve a Krein space induced fundamental symmetry operator, J, while some of these generalized relations involve an anti-commutator, a commutator, and various other nonlinear functions of the two operators in question. As a consequence there exist classes of non-self-adjoint operators on Hilbert spaces such that the non-vanishing of their commutator implies an uncertainty relation. All relations include the classical Heisenberg uncertainty principle as formulated in Hilbert Space by Von Neumann and others. In addition, we derive an operator dependent (nonlinear) commutator uncertainty relation in Krein space.