2004/10/20 by C. Chryssomalakos, C. CHRYSSOMALAKOS, E. Okon +1 · 58 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Deformation (meteorology) #Invariant (physics) #Kinematics #Lie algebra #Noncommutative and Quantum Gravity Theories #Position (finance) #Quantum #Quantum field theory in curved spacetime #Quantum spacetime #Spacetime #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1142/s0218271804006632
published in International Journal of Modern Physics D 13(10), 2003-2034 (World Scientific) · 26 pages, 2 figures
arxiv created 2004/10/20 · openalex publication_date 2004/12/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We apply Lie algebra deformation theory to the problem of identifying the stable form of the quantum relativistic kinematical algebra. As a warm up, given Galileo's conception of spacetime as input, some modest computer code we wrote zeroes in on the Poincaré-plus-Heisenberg algebra in about a minute. Further ahead, along the same path, lies a three-dimensional deformation space, with an instability double cone through its origin. We give physical as well as geometrical arguments supporting our view that moment, rather than position operators, should enter as generators in the Lie algebra. With this identification, the deformation parameters give rise to invariant length and mass scales. Moreover, standard quantum relativistic kinematics of massive, spinless particles corresponds to non-commuting moment operators, a purely quantum effect that bears no relation to spacetime non-commutativity, in sharp contrast to earlier interpretations.