8,212 research outputs found
Relational time in generally covariant quantum systems: four models
We analize the relational quantum evolution of generally covariant systems in
terms of Rovelli's evolving constants of motion and the generalized Heisenberg
picture. In order to have a well defined evolution, and a consistent quantum
theory, evolving constants must be self-adjoint operators. We show that this
condition imposes strong restrictions to the choices of the clock variables. We
analize four cases. The first one is non- relativistic quantum mechanics in
parametrized form. We show that, for the free particle case, the standard
choice of time is the only one leading to self-adjoint evolving constants.
Secondly, we study the relativistic case. We show that the resulting quantum
theory is the free particle representation of the Klein Gordon equation in
which the position is a perfectly well defined quantum observable. The
admissible choices of clock variables are the ones leading to space-like
simultaneity surfaces. In order to mimic the structure of General Relativity we
study the SL(2R) model with two Hamiltonian constraints. The evolving constants
depend in this case on three independent variables. We show that it is possible
to find clock variables and inner products leading to a consistent quantum
theory. Finally, we discuss the quantization of a constrained model having a
compact constraint surface. All the models considered may be consistently
quantized, although some of them do not admit any time choice such that the
equal time surfaces are transversal to the orbits.Comment: 18 pages, revtex fil
Beables/Observables in Classical and Quantum Gravity
Observables 'are observed' whereas beables just 'are'. This gives beables
more scope in the cosmological and quantum domains. Both observables and
beables are entities that form 'brackets' with 'the constraints' that are
'equal to' zero. We explain how depending on circumstances, these could be,
e.g., Poisson, Dirac, commutator, histories, Schouten-Nijenhuis, double or
Nambu brackets, first-class, gauge, linear or effective constraints, and
strong, weak or weak-effective equalities. The Dirac-Bergmann distinction in
notions of gauge leads to further notions of observables or beables, and is
tied to a number of diffeomorphism-specific subtleties. Thus we cover a wide
range of notions of observables or beables that occur in classical and quantum
gravitational theories: Dirac, Kucha\v{r}, effective, Bergmann, histories,
multisymplectic, master, Nambu and bi-. Indeed this review covers a
representatively wide range of such theories: general relativity, loop quantum
gravity, histories theory, supergravity and M-theory
Algebraic optimization of recursive queries
Over the past few years, much attention has been paid to deductive databases. They offer a logic-based interface, and allow formulation of complex recursive queries. However, they do not offer appropriate update facilities, and do not support existing applications. To overcome these problems an SQL-like interface is required besides a logic-based interface.\ud
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In the PRISMA project we have developed a tightly-coupled distributed database, on a multiprocessor machine, with two user interfaces: SQL and PRISMAlog. Query optimization is localized in one component: the relational query optimizer. Therefore, we have defined an eXtended Relational Algebra that allows recursive query formulation and can also be used for expressing executable schedules, and we have developed algebraic optimization strategies for recursive queries. In this paper we describe an optimization strategy that rewrites regular (in the context of formal grammars) mutually recursive queries into standard Relational Algebra and transitive closure operations. We also describe how to push selections into the resulting transitive closure operations.\ud
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The reason we focus on algebraic optimization is that, in our opinion, the new generation of advanced database systems will be built starting from existing state-of-the-art relational technology, instead of building a completely new class of systems
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