Showing papers on "Quantum geometry published in 1984"
TL;DR: In this article, the quantum statistics of linear and nonlinear optical Phenomena are presented. But they do not consider the non-linear optical properties of the optical components of the system.
Abstract: (1984). Quantum Statistics of Linear and Nonlinear Optical Phenomena. Optica Acta: International Journal of Optics: Vol. 31, No. 8, pp. 847-847.
89 citations
TL;DR: In this article, a theory physically equivalent to traditional nonrelativistic quantum mechanics is presented, in which both dynamical and probabilistic concepts enter in a classical way.
Abstract: A theory physically equivalent to traditional nonrelativistic quantum mechanics is presented, in which both dynamical and probabilistic concepts enter in a classical way. Particle trajectories are deterministically governed by classical mechanics, only the initial position being at random. Quantum effects are supposed to arise from a modification of the geometry of space, due to the presence of matter. However, unlike gravitational forces, which are related to the metric of space-time, quantum-mechanical forces are proved to be related to the transplantation law of vectors. The resulting geometry of space, in the nonrelativistic limit, is found to be Weyl's geometry. Both particle motion and geometry of space are obtained from a unique averaged least-action principle.
87 citations
84 citations
TL;DR: In this paper, a general method is presented for constructing Kaluza-Klein instantons based on solutions of ordinary Yang-Mills theory, which can be used to perform explicit semiclassical calculations of the effects of space-time foam.
52 citations
TL;DR: In this article, it is shown that a model with two degrees of freedom, corresponding to a metric and a connection variable, has a sensible high energy limit, while a related model, in which a constraint analogous to metric compatibility is imposed, is found to be unstable at high energies.
16 citations
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TL;DR: The quantum simplex as mentioned in this paper is a quantum simplicial topology suitable for a quantum theory of time space and gravity without prior time space structure; it is isotropic and all quantum simplexes of the same signature are congruent.
Abstract: Quantum set theory permits the formulation of a quantum simplicial topology suitable for a quantum theory of time space and gravity without prior time space structure. The quantum simplex differs strikingly from the classical: It is isotropic (“points in all directions”) and all quantum simplexes of the same signature are congruent. Quantum simplexes and complexes are described byS numbers, elements of the Clifford algebra of quantum sets. The isotropy groups of noncontiguous simplexes commute, like local invariance groups in a gaugeinvariant theory.
12 citations
TL;DR: In this paper, the law of propagation for light has the same form for all macroscopic observers, i.e., observers who may be large, but not infinitely large, by comparison with quantum mechanical systems.
Abstract: The relativity principle that the law of propagation for light has the same form for all macroscopic observers is extended to include quantum observers; i.e., observers who may be large, but not infinitely large, by comparison with quantum mechanical systems. This leads to the extension of the covariance group from the diffeomorphisms to the conservation group (which is the largest group of coordinate transformations under which conservation laws are covariant statements) and, thus, to the quantum geometry and quantum unified field theory considered in a previous paper.
10 citations
TL;DR: In this article, the mathematical properties of asymptotic operators obtained are applied to establish an algebraic formulation of quantum mechanics, which has the characteristic of being asymptonically separable.
Abstract: The asymptotic behaviour of quantum mechanical states at large times has been discussed in two recent papers by Wan and McLean (1983). In a third paper a detailed study of the corresponding behaviour of observables was made. The mathematical properties of asymptotic operators obtained are applied in this paper to establish an algebraic formulation of quantum mechanics which has the characteristic of being asymptotically separable. The age-old non-locality problem in quantum mechanics can then be effectively tackled.
10 citations
TL;DR: In this article, a stochastic phase-space solution of the particle localizability problem in relativistic quantum mechanics is reviewed, which leads to relativistically covariant probability measures that give rise to covariant and conserved probability currents.
Abstract: The stochastic phase-space solution of the particle localizability problem in relativistic quantum mechanics is reviewed. It leads to relativistically covariant probability measures that give rise to covariant and conserved probability currents. The resulting particle propagators are used in the formulation of stochastic geometries underlying a concept of quantum spacetime that is operationally based on stochastically extended quantum test particles. The epistemological implications of the intrinsic stochasticity of such quantum spacetime frameworks for microcausality, the EPR paradox, etc., are discussed.
9 citations
TL;DR: In this article, the causal description with action at a distance for two-particle systems in EPR types of experiments was generalized to a system of N scalar particles. And the many-body quantum potential was shown to satisfy the predictivity constraints established by Droz-Vincent for relativistic mechanics.
Abstract: We generalize to a system ofN scalar particles the causal description with action at a distance already given for two-particle systems in EPR types of experiments. The many-body quantum potential is shown to satisfy the predictivity constraints established by Droz-Vincent for relativistic mechanics.
TL;DR: The change in the meaning of observables and states in quantum physics as compared with classical physics is discussed and shown to account for the novel formal properties of quantum observables as mentioned in this paper.
Abstract: The change in the meaning of observables and states in quantum physics as compared with classical physics is discussed and shown to account for the novel formal properties of quantum observables and states. The special character of observation interactions in quantum physics, in particular the discontinuous reductions of state vectors during measurements, is readily understood if the novel meaning of quantum states is taken into account.
TL;DR: In this paper, the focus is not on finding the direct solution to the equations of quantum field theory, but rather on developing an effective and reliable method for evaluating the functional integrals representing the Green's functions.
Abstract: Many of the approaches to numerical quantum field theory which have been developed to date start from the Euclidean path integral formulation of the theory. This is because it is possible, using path integrals, to write closed form, albeit formal and difficult to evaluate, expressions for the quantities of physical interest, namely the Green’s functions. Thus, in this approach, the focus is not on finding the direct solution to the equations of quantum field theory, but rather on developing an effective and reliable method for evaluating the functional integrals representing the Green’s functions.
TL;DR: The mathematical problem of the existence of the mean value and variance of unbounded observables is studied in this paper, where the authors consider both pure states and quantum mixtures, with particular care for the problems that arise in the latter case.
Abstract: In this paper we examine, in the framework of Hilbert-space quantum mechanics, the mathematical problem of the existence of the mean value and variance of unbounded observables. We consider both pure states and quantum mixtures, with particular care for the problems that arise in the latter case.
TL;DR: In this paper, the superhamiltonian constraint is explicitly rewritten as an operator equation acting on the coordinate invariant functionals, which are constructed in 2-dimensional space and 2-space dimensions.
TL;DR: In this paper, the results of Babellon and Viallet on a possible geometrical interpretation of the Faddeev-Popov functional measure for Yang-Mills theories are adapted to the case of pure quantum gravity.
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01 Aug 1984TL;DR: In this paper, the authors describe several studies dealing with these aspects: failure of popular ad hoc chemical concepts underab initio scrutiny, failure of AB initio calculations to provide simple concepts, and highly attractive concepts and pictures generated by the electron density in 3D space.
Abstract: There are three reasons for seeking an alternative density-based quantum mechanics of many-electron systems, incorporating both interpretive and basic quantum mechanical aspects: (i) failure of popularad hoc chemical concepts underab initio scrutiny; (ii) failure ofab initio calculations to provide simple concepts; and (iii) highly attractive concepts and pictures generated by the electron density in three-dimensional space. At present the three interlinked pillars for such a density mechanics (in contrast to wave mechanics) are: (a) density functional theory; (b) quantum fluid dynamics; and (c) property densities in three-dimensional space. This article describes several studies dealing with these aspects. Although a density mechanics may well be an impossible ideal to realize, the search for it is indeed rejuvenating the whole of quantum chemistry.
01 Jan 1984
TL;DR: The workshop D1, "Quantum Gravity" as mentioned in this paper was divided into two parts, the first and the longer part devoted to a review of major developments that have occurred in recent years, while the second part was concerned more with directions for future.
Abstract: The workshop D1, ‘Quantum Gravity’, was divided into two parts. The first and the longer part was devoted to a review of major developments that have occurred in recent years(1) while the second part was concerned more with directions for future. The review talks were given by Bernard Kay (Quantum Field Theory in curved space-times) Andy Strominger (Higher Derivative Quantum Gravity), Rafael Sorkin(2) (Global and Topological Aspects of Quantum Gravity), and, Lee Smolin (Conceptual problems in Quantum Gravity), and several directions for future work in the area were suggested by Jim Hartle, John Klauder, David Finkelstein and Roger Penrose.