4,092 research outputs found
A Possible Extension of a Trial State in the TDHF Theory with Canonical Form in the Lipkin Model
With the aim of the extension of the TDHF theory in the canonical form in the
Lipkin model, the trial state for the variation is constructed, which is an
extension of the Slater determinant. The canonicity condition is imposed to
formulate the variational approach in the canonical form. A possible solution
of the canonicity condition is given and the zero-point fluctuation induced by
the uncertainty principle is investigated. As an application, the ground state
energy is evaluated.Comment: 15 pages, 1 figure, using PTPTeX styl
Canonical Truth
We introduce and study a notion of canonical set theoretical truth, which
means truth in a `canonical model', i.e. a transitive class model that is
uniquely characterized by some -formula. We show that this notion of truth
is `informative', i.e. there are statements that hold in all canonical models
but do not follow from ZFC, such as Reitz' ground model axiom or the
nonexistence of measurable cardinals. We also show that ZF++AD
has no canonical models. On the other hand, we show that there are canonical
models for `every real has sharp'. Moreover, we consider `theory-canonical'
statements that only fix a transitive class model of ZFC up to elementary
equivalence and show that it is consistent relative to large cardinals that
there are theory-canonical models with measurable cardinals and that
theory-canonicity is still informative in the sense explained above
Abstract Canonical Inference
An abstract framework of canonical inference is used to explore how different
proof orderings induce different variants of saturation and completeness.
Notions like completion, paramodulation, saturation, redundancy elimination,
and rewrite-system reduction are connected to proof orderings. Fairness of
deductive mechanisms is defined in terms of proof orderings, distinguishing
between (ordinary) "fairness," which yields completeness, and "uniform
fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi
Modalities, Cohesion, and Information Flow
It is informally understood that the purpose of modal type constructors in
programming calculi is to control the flow of information between types. In
order to lend rigorous support to this idea, we study the category of
classified sets, a variant of a denotational semantics for information flow
proposed by Abadi et al. We use classified sets to prove multiple
noninterference theorems for modalities of a monadic and comonadic flavour. The
common machinery behind our theorems stems from the the fact that classified
sets are a (weak) model of Lawvere's theory of axiomatic cohesion. In the
process, we show how cohesion can be used for reasoning about multi-modal
settings. This leads to the conclusion that cohesion is a particularly useful
setting for the study of both information flow, but also modalities in type
theory and programming languages at large
A different perspective on canonicity
One of the most interesting aspects of Conceptual Structures Theory is the notion of canonicity. It is also one of the most neglected: Sowa seems to have abandoned it in the new version of the theory, and most of what has been written on canonicity focuses on the generalization hierarchy of conceptual graphs induced by the canonical formation rules. Although there is a common intuition that a graph is canonical if it is "meaningful'', the original theory is somewhat unclear about what that actually means, in particular how canonicity is related to logic. This paper argues that canonicity should be kept a first-class notion of Conceptual Structures Theory, provides a detailed analysis of work done so far, and proposes new definitions of the conformity relation and the canonical formation rules that allow a clear separation between canonicity and truth
Solution of the noncanonicity puzzle in General Relativity: a new Hamiltonian formulation
We study the transformation leading from Arnowitt, Deser, Misner (ADM)
Hamiltonian formulation of General Relativity (GR) to the metric
Hamiltonian formulation derived from the Lagrangian density which was firstly
proposed by Einstein. We classify this transformation as gauged canonical -
i.e. canonical modulo a gauge transformation. In such a study we introduce a
new Hamiltonian formulation written in ADM variables which differs from the
usual ADM formulation mainly in a boundary term firstly proposed by Dirac.
Performing the canonical quantization procedure we introduce a new functional
phase which contains an explicit dependence on the fields characterizing the
3+1 splitting. Given a specific regularization procedure our new formulation
privileges the symmetric operator ordering in order to: have a consistent
quantization procedure, avoid anomalies in constraints algebra, be equivalent
to the Wheeler-DeWitt (WDW) quantization. Furthermore we show that this result
is consistent with a path-integral approach.Comment: Accepted for Publication in Physics Letters B. Major revisions in
Canonical Quantization section for operator ordering choice and in the
definition of 'gauged canonicity' for the classical analysis. 19 pages single
colum
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