Showing papers on "Quantum geometry published in 1974"
TL;DR: In this paper, the formalism of covariant conditional expectations is described as leading to an operational definition of generalized observables in quantum mechanics, wide enough to account for the fuzziness inherent in actual measurement processes, relative to a multidimensional physical continuum.
Abstract: The formalism of covariant conditional expectations is described as leading to an operational definition of generalized observables in quantum mechanics, wide enough to account for the fuzziness inherent in actual measurement processes, relative to a multidimensional physical continuum. As an application, a position operator for the photon is defined and its intrinsic fuzziness is discussed.
113 citations
52 citations
TL;DR: In this paper, Hamilton's quaternions resurface once again to suggest relativistic generalizations of quantum theory and a new spin-12 wave equation, and they are used for vector analysis.
Abstract: Hamilton's ancient quaternion formalism gave rise to vector analysis. Quaternions resurface once again to suggest relativistic generalizations of quantum theory and a new spin-12 wave equation.
35 citations
27 citations
26 citations
TL;DR: In this article, it was shown that potentials in force-free regions have not only a nonlocal physically measurable significance (via, e.g., ∮A ·dl), but also have a necessary local significance via their quantum spread ΔA.
Abstract: In a sequel to our previous paper we discuss two thought experiments which show that potentials in force-free regions have not only a nonlocal physically measurable significance (via, e.g., ∮A ·dl), but, in singly connected portions of that region, also have a necessary local significance (via their quantum spread ΔA, which cannot be neglected). We then show, in continuation to the foregoing paper, how suchA arise “geometrically” as kinematic quantities associated with the transformation between “quantum-related” reference frames, e.g., when the relative frame velocities areq-numbers possessing a quantum spread.
21 citations
TL;DR: In this paper, the transformation theory of nonrelativistic quantum mechanics within the framework of rigged Hilbert spaces is studied, and results of a previous paper are used to obtain a rigorous mathematical formulation.
Abstract: Results of a previous paper are used to obtain a rigorous mathematical formulation of the transformation theory of nonrelativistic quantum mechanics within the framework of rigged Hilbert spaces.
18 citations
6 citations
TL;DR: In this article, a representation of the position and angular-momentum variables of a quantum-mechanical rigid rotator is obtained from general symmetry principles, similar to the treatment of spin in the case of the quantum particle.
Abstract: A representation of the position and angular-momentum variables of a quantum-mechanical rigid rotator is obtained from general symmetry principles. The method used is similar to the treatment of spin in the case of the quantum particle.
4 citations
TL;DR: In this article, the authors used homological algebra to derive some results in the theory of Lie groups, which they used in their paper "Homological Algebra for Lie Group Theory".
Abstract: Homological algebra is used to derive some results in the theory of Lie groups.
1 citations
Journal Article•
TL;DR: In this article, the authors considered linearized deviations from two kinds of hypersurfaces of a de Sitter universe and the ground state functionals of these deviations were described, which was the approach used by Kuchar in his study of the linearized gravitational field.
Abstract: Linearized deviations from two kinds of hypersurfaces of a de Sitter universe are considered. Ground state functionals of these deviations are described. The approach is the one used by Kuchar in his study of the linearized gravitational field. RESUME. On considere deux sortes d’hypersurfaces de l’univers de de Sitter et leurs deviations linearisces. Les fonctionnelles fondamentales de ces deviations sont decrites. On aborde ce probleme par la methode employee par Kuchar dans son etude du champ gravitationnel linearise.