16,387 research outputs found
Translocality and a Duality Principle in Generally Covariant Quantum Field Theory
It is argued that the formal rules of correspondence between local
observation procedures and observables do not exhaust the entire physical
content of generally covariant quantum field theory. This result is obtained by
expressing the distinguishing features of the local kinematical structure of
quantum field theory in the generally covariant context in terms of a
translocal structure which carries the totality of the nonlocal kinematical
informations in a local region. This gives rise to a duality principle at the
dynamical level which emphasizes the significance of the underlying translocal
structure for modelling a minimal algebra around a given point. We discuss the
emergence of classical properties from this point of view.Comment: 12 pages. To appear in Classical Quantum Gravit
Godel's Incompleteness Phenomenon - Computationally
We argue that Godel's completeness theorem is equivalent to completability of
consistent theories, and Godel's incompleteness theorem is equivalent to the
fact that this completion is not constructive, in the sense that there are some
consistent and recursively enumerable theories which cannot be extended to any
complete and consistent and recursively enumerable theory. Though any
consistent and decidable theory can be extended to a complete and consistent
and decidable theory. Thus deduction and consistency are not decidable in
logic, and an analogue of Rice's Theorem holds for recursively enumerable
theories: all the non-trivial properties of such theories are undecidable
Separating Bounded Arithmetics by Herbrand Consistency
The problem of separating the hierarchy of bounded arithmetic has
been studied in the paper. It is shown that the notion of Herbrand Consistency,
in its full generality, cannot separate the theory from ; though it can
separate from . This extends a
result of L. A. Ko{\l}odziejczyk (2006), by showing the unprovability of the
Herbrand Consistency of in the theory .Comment: Published by Oxford University Press. arXiv admin note: text overlap
with arXiv:1005.265
A New Method for Obtaining the Baryons Mass under the Killingbeck Plus Isotonic Oscillator Potentials
In this work, the spectrum of ground state and excited baryons (N, {\Delta},
, , and {\Omega} particles) has been investigated by using a non-relativistic
quantum mechanics under the Killingbeck plus isotonic oscillator potentials.
Using the Jacobi-coordinates, anzast method and generalized G\"ursey Radicati
(GR) mass formula the three body wave equation is solved to calculate the
different states of the considered baryons. A comparison between our
calculations and the available experimental data shows that the position of the
Roper resonances of the nucleon, the ground states and the excited multiplets
up to three GeV are in general well reproduced. Also one can conclude that; the
interaction between the quark constituents of baryon resonances could be
described adequately by using the combination of Killingbeck and isotonic
oscillator potentials form.Comment: arXiv admin note: text overlap with arXiv:nucl-th/0506032 by other
author
Herbrand Consistency of Some Arithmetical Theories
G\"odel's second incompleteness theorem is proved for Herbrand consistency of
some arithmetical theories with bounded induction, by using a technique of
logarithmic shrinking the witnesses of bounded formulas, due to Z. Adamowicz
[Herbrand consistency and bounded arithmetic, \textit{Fundamenta Mathematicae}
171 (2002) 279--292]. In that paper, it was shown that one cannot always shrink
the witness of a bounded formula logarithmically, but in the presence of
Herbrand consistency, for theories with , any witness for any bounded formula can be shortened logarithmically. This
immediately implies the unprovability of Herbrand consistency of a theory
in itself.
In this paper, the above results are generalized for . Also after tailoring the definition of Herbrand
consistency for we prove the corresponding theorems for . Thus the Herbrand version of G\"odel's second incompleteness
theorem follows for the theories and
Russian foreign policy: The return of great power politics
In Russian Foreign Policy: The Return of Great Power Politics, Jeffrey Mankoff examines the course of Russian foreign policy since the dissolution of the Soviet Union in 1991. He provides a comprehensive over-view of both the continuity and the changes in Russian foreign policy from the end of the Cold War to the Putin era, and analyses Russia’s interactions with major global powers. Throughout the book, the author makes use of various theoretical approaches, including theories of international relations, classical geopolitical theory and Russian geopolitical tradition
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