2005/08/31 by Peter Jarvis, P D Jarvis, S O Morgan +1 · 2 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Hamiltonian (control theory) #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Semiclassical physics #Spacetime #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s10702-006-1006-5
published as Found.Phys.Lett.19:501-517,2006 · 12 pages, LaTeX. Minor wording changes and references updated
arxiv created 2005/10/14 · openalex publication_date 2006/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Schrödinger-Robertson inequality for relativistic position and momentum operators Xμ, Pν, μ, ν= 0,1,2,3, is interpreted in terms of Born reciprocity and `non-commutative' relativistic phase space geometry. For states which saturate the Schrödinger-Robertson inequality, a typology of semiclassical limits is pointed out, characterised by the orbit structure within its unitary irreducible representations, of the full invariance group of Born reciprocity, the so-called `quaplectic' group U(3,1)xH(3,1) (the semi-direct product of the unitary relativistic dyamical symmetry U(3,1) with the Weyl-Heisenberg group H(3,1)). The example of the `scalar' case, namely the relativistic oscillator, and associated multimode squeezed states, is treated in detail. In this case,it is suggested that the semiclassical limit corresponds to the separate emergence of space-time and matter, in the form of the stress-energy tensor, and the quadrupole tensor, which are in general reciprocally equivalent.