Showing papers on "Quantum geometry published in 1987"
TL;DR: In this paper, it was shown that it is impossible to measure the position of a particle to an accuracy better than the Planck length (G/c3) approximately = 10-33 cm.
Abstract: Using simple arguments from general relativity and quantum theory the author shows that it is not possible to devise experiments (or operational procedures) which will measure the position of a particle to an accuracy better then the Planck length (G/c3) approximately=10-33 cm. It is also impossible to synchronise clocks to a precision better than Planck time. The implications of the result are discussed.
194 citations
Journal Article•
162 citations
TL;DR: In this paper, the classical and quantum versions of discrete mechanics are reviewed and applications to lattice field theory and quantum gravity are considered, with a focus on lattice fields and quantum mechanics.
Abstract: The classical and quantum versions of discrete mechanics are reviewed. Application to lattice field theory and quantum gravity are considered. (AIP)
84 citations
Book•
30 Nov 1987
TL;DR: In this article, the Bohr-Rosenfeld principles of measurement in Quantum Field Theory are discussed. But they do not consider the effect of the Compton Effect on quantum field theory.
Abstract: 1/Quantum Theory and Gravitation.- 2/Quantum Mechanics and Classical Gravitation.- 2.1. Diffraction of Particles by a Grating.- 2.2. Diffraction of Particles by a Gravitational Grating.- 2.3. Gravitational Atomic Model.- 2.4. Equivalence Principle and Heisenberg's Fourth Relation.- 2.5. Quantum Mechanics and the Weak Principle of Equivalence.- 3/Measurement in Quantum Gravity.- 3.1. The Bohr-Rosenfeld Principles of Measurement in Quantum Field Theory.- (a) The Landau-Peierls Arguments.- (b) The Bohr-Rosenfeld Arguments.- 3.2. Measurement in Quantum Gravity.- 3.3. Ehrenfest's Theorems.- 4/Mathematical Descriptions of Quantum Gravity.- 4.1. Heisenberg-Euler-Kockel Approximation.- 4.2. On Gauge Fixing in Quantum Gravity.- 5/Quantum Postulates and the Strong Principle of Equivalence.- 5.1. Gravitons and the Linear Approximation of General Relativity Theory.- 5.2. Gravitons and the Nonlinear High-Frequency Approximation of General Relativity Theory.- 5.3. Compton Effect.- 5.4. Lamb Shift.- 5.5. Black-body Radiation.- 5.6. A Historical Remark: Black-body Radiation and Compton Effect.- 6/Planckions.- 6.1. Heavy Gravitons.- 6.2. Planckions as Biggest Elementary Particles and as Smallest Test Bodies.- 6.3. Foam and Block Spaces.- Appendix A/Massive Shell Models and Shock Waves in Gravitational Theories with Higher Derivatives.- Appendix B/On the Physical Meaning of Planck's 'Natural Units'.- References.
77 citations
TL;DR: In this paper, an analogy between the Veneziano amplitude and the p-adic interpolation of the beta function is suggested as the basis of a new padic quantum geometry, and relationships with the Weil conjectures, Fermat curves and anomalies are discussed.
57 citations
TL;DR: In this paper, a rigorous path integral treatment of free motion on the Poincare upper half plane is presented, where the energy spectrum and the normalized wavefunctions are determined by a canonical method for determining quantum corrections to the classical lagrangian.
37 citations
01 Jan 1987
TL;DR: In the early universe, however, the classical approximation is unlikely to be valid as discussed by the authors, since quantum fluctuations become important and eventually dominant in the Planck length curvatures of the universe.
Abstract: As far as we know them, the fundamental laws of physics are quantum mechanical in nature. If these laws apply to the universe as a whole, then there must be a description of the universe in quantum mechancial terms. Even our present cosmological observations require such a description in principle, although in practice these observations are so limited and crude that the approximation of classical physics is entirely adequate. In the early universe, however, the classical approximation is unlikely to be valid. There, towards the big bang singularity, at curvatures characterized by the Planck length, (ћG/c 3)1/2 , quantum fluctuations become important and eventually dominant.
34 citations
TL;DR: In this article, the authors formulate a general-relativistic concept of quantum geometry capable of describing the behaviour of quantum Lorentz frames in free fall in arbitrary external gravitational fields.
Abstract: We formulate a general-relativistic concept of quantum geometry capable of describing the behaviour of quantum Lorentz frames in free fall in arbitrary external gravitational fields. The mathematical framework suited to this task turns out to be that of Hilbert bundles over a space-time manifold of mean stochastic locations of quantum test particles, with fibres soldered to the base manifold at each given mean space-time location. Furthermore, these fibre bundles incorporate connections compatible with the Hermitian structure. Quantum propagation results from the parallel transport governed by these connections and applied to generalized coherent states, whereas the Hermitian structure supplies the transition probabilities required for the construction of quantum frame and particle propagators. All resulting fibre bundles are shown to possess nonzero curvature forms, which in the generic case incorporate the symplectic 2-form of the cotangent bundle of the base manifold, the pseudo-Riemannian curvature of that manifold and additional components resulting from Maxwell and Yang-Mills connections. In addition, their structure groups incorporate stochastic phase space representations of the Poincare group in a manner that supplies manifest Poincare gauge invariance of the resulting quantum space-time framework.
24 citations
22 citations
TL;DR: In this paper, the role of quantum Lorentz frame is taken over by second-quantized frames constructed out of coherent exciton states, whose structure groups contain unitary representations of the Poincare group, with the latter emerging as a gauge group for the internal degrees of freedom of the considered quantum particles.
Abstract: It is shown that an earlier introduced concept of quantum geometry, given by a Hilbert bundle over a base space whose elements constitute a generic curved space-time and represent the mean locations of quantum frames, can be generalized to the case of Fock bundles, whose Fock fibres are the carriers of multiparticle states In this new context, the role of quantum Lorentz frame is taken over by second-quantized frames constructed out of coherent exciton states The structure groups of the considered bundles contain unitary representations of the Poincare group, with the latter emerging as a gauge group for the internal degrees of freedom of the considered quantum particles Connections compatible with the Hermitian structure are introduced on bundles of second-quantized frames that are associated to principal bundles of affine Lorentz frames The corresponding parallel transport is expressed in terms of path integrals for quantum frame propagators It is shown that the resulting geometro-stochastic quantum field theory in curved space-time does not give rise to the foundational difficulties with the particle concept, with normal ordering and with the definition of the stress-energy tensor, that are inherent in more conventional approaches to quantum field theory in curved space-time Hence, the derived path integral formulae for the propagation of systems of quantum field particles display in the present framework none of the ambiguities encountered by those approaches
14 citations
01 Jan 1987
TL;DR: In this article, the theoretical and observational aspects for the topology of the universe are discussed to show that the significances of topology in present observations can shed some light on the properties of universe in the quantum cosmological era.
Abstract: Topology of the universe is the remains of quantum cosmology. The theoretical and observational aspects for the topology of the universe are discussed to show that the significances of topology of the universe in present observations can shed some light on the properties of the universe in the quantum cosmological era.
TL;DR: In this paper, it was shown within the Hilbert space formulation of quantum mechanics that the total noncommutativity of any two physical quantities is necessary for their satisfying the uncertainty relation or for their being complementary.
Abstract: It is shown within the Hilbert space formulation of quantum mechanics that the total noncommutativity of any two physical quantities is necessary for their satisfying the uncertainty relation or for their being complementary. The importance of these results is illustrated with the canonically conjugate position and momentum of a free particle and of a particle closed in a box.
TL;DR: In this paper, a degree theory for Wiener maps is developed for path integrals for supersymmetric Hamiltonians in quantum mechanics, and an application of this theory is given in the study of path integral for super-SUHMs.
01 Jul 1987
TL;DR: In this article, the Green function was found for the quantum fluctuations near the classical instanton configuration, which was used for calculation of the distortion of the form of the instanton due to the non-Gauss effects.
Abstract: The Green function is found for the quantum fluctuations near the classical instanton configuration. This function is used for calculation of the distortion of the form of the instanton due to the non-Gauss effects and for the calculation of correction to the instanton density (tunnelling probability).
TL;DR: In this article, the kink sector of the 24 quantum field theory in the broken-symmetry phase was constructed using Euclidean methods, and the construction exhibits relations with differential geometry and statistical mechanics.
Abstract: We construct the kink sector of the 24 quantum field theory, in the broken-symmetry phase, using Euclidean methods. The construction exhibits relations with differential geometry and statistical mechanics. In particular we prove that the Euclidean Green's functions of kinks are obtained by integration over section distributions of nontrivial bundles and are well defined as Jaffe ultradistributions.
TL;DR: In this paper, quantum effects are incorporated into the gravitational dynamics in the vicinity of singularity in the case of three important general relativistic spacetimes, namely the spherically symmetric dust-ball collapse, standard Friedmann models and a general cosmological scenario given by Belinskii et al.
Abstract: We incorporate quantum effects into the gravitational dynamics in the vicinity of singularity in the case of three important general relativistic spacetimes, namely the spherically symmetric dust-ball collapse, standard Friedmann models and a general cosmological scenario given by Belinskii et al. The quantum state of the universe is represented by a general wave function where the conformal degree of freedom is quantised. It is seen in each case that the spread around the classical state diverges in the limit of approach to the classically singular epoch. Thus, non-classical, non-singular states can occur with finite probability. Our results show that including quantum effects radically changes the usual singularity scenario.
TL;DR: It is shown how the exact solvability of some of the well-known one-dimensional quantum systems arises from an underlying SU(2) dynamical symmetry.
Abstract: We show how the exact solvability of some of the well-known one-dimensional quantum systems arises from an underlying SU(2) dynamical symmetry.
TL;DR: In this paper, a cosmological model is proposed, in which quantum effects lead to infinitely many terms nonlinear in curvature, and these terms lead to the following conclusion: the physical singularity (i.e., a state with infinite matter densityp) occurs int≃10−43 s, when the curvature is finite
Abstract: A cosmological model is proposed, in which quantum effects lead to infinitely many terms nonlinear in curvature, and these terms lead to the following conclusion: the physical singularity (ie, a state with infinite matter densityp) occurs int≃10−43 s, when the curvature is finite An attempt is made to give physical interpretation of this model from the viewpoint of the ‘foam-like’ model of space-time
01 Jan 1987
TL;DR: In this paper, an example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local, and initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity.
Abstract: An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity.
01 Jan 1987
TL;DR: In this paper, a review of recent developments in one aspect of this subject and to point out a number of unexpected relationships is presented. But the results and ideas discussed here were obtained in collaboration with B. Osgood and R. Phillips and appear in the paper [O-P-S].
Abstract: In modern quantum geometry of strings and especially in the so-called Polyakov string model [P] determinants of Laplacians play a crucial role. As a result the study of this quantity and in particular its dependence on the metric, has been very productive. Our aim here is to review some recent developments in one aspect of this subject and to point out a number of unexpected relationships. Many of the results and ideas discussed here were obtained in collaboration with B. Osgood and R. Phillips and appear in the paper [O-P-S].
TL;DR: The relation between the Christodoulakis-Zanelli Schwinger term in the commutators of the constraints and the Weyl diffeomorphism cocycle is discussed in this paper.
TL;DR: In this paper, it is suggested to take the topological properties of compact riemannian surfaces more completely into account in the quantum geometry of strings, by using the fact that linear real bundles over any manifold and spinorial structures on it are both classified by the same cohomology group H 1 (M; Z 2 ).
01 Jan 1987
TL;DR: Canonical quantum gravity can be reduced in a semi-classical limit to conventional quantum gravity on a curved spacetime background as discussed by the authors, which introduces density matrices or nonlinear terms into the semi classical limit.
Abstract: Canonical quantum gravity can be reduced in a semi-classical limit to conventional quantum gravity on a curved spacetime background. Changes in the topology of space require a reformulation of the theory which introduces density matrices or nonlinear terms into the semi-classical limit.
TL;DR: It turns out that almost all the initial conditions for scale factor of the universe a = 0 for quantum states (wave functions) of free scalar fields in the de Sitter metric with imaginary t give the same quantum state.
Abstract: The initial-value problem for scale factor of the universe a=0 for quantum states (wave functions) of free scalar fields in the de Sitter metric a\ensuremath{\propto}cosh(ht) with imaginary t is studied. It turns out that almost all the initial conditions give the same quantum state. Some effects of the quantization of the metric are also discussed.