Immirzi Ambiguity in the Kinematics of Quantum General Relativity

The Immirzi ambiguity arises in loop quantum gravity when geometric operators are represented in terms of different connections that are related by means of an extended Wick transform. We analyze the action of this transform in gravity coupled with matter fields and discuss its analogy with the Wick rotation on which the Thiemann transform between Euclidean and Lorentzian gravity is based. In addition, we prove that the effect of this extended Wick transform is equivalent to a constant scale transformation as far as the symplectic structure and kinematical constraints are concerned. This equivalence is broken in the dynamical evolution. Our results are applied to the discussion of the black hole entropy in the limit of large horizon areas. We first argue that, since the entropy calculation is performed for horizons of fixed constant area, one might in principle choose an Immirzi parameter that depends on this quantity. This would spoil the linearity with the area in the entropy formula. We then show that the Immirzi parameter appears as a constant scaling in all the steps where dynamical information plays a relevant role in the entropy calculation. This fact, together with the kinematical equivalence of the Immirzi ambiguity with a change of scale, is used to preclude the potential non-linearity of the entropy on physical grounds.Comment: very minor stylistic changes, version published in Phys. Rev.

The Chrono-geometrical Structure of Special and General Relativity: a Re-Visitation of Canonical Geometrodynamics

A modern re-visitation of the consequences of the lack of an intrinsic notion of instantaneous 3-space in relativistic theories leads to a reformulation of their kinematical basis emphasizing the role of non-inertial frames centered on an arbitrary accelerated observer. In special relativity the exigence of predictability implies the adoption of the 3+1 point of view, which leads to a well posed initial value problem for field equations in a framework where the change of the convention of synchronization of distant clocks is realized by means of a gauge transformation. This point of view is also at the heart of the canonical approach to metric and tetrad gravity in globally hyperbolic asymptotically flat space-times, where the use of Shanmugadhasan canonical transformations allows the separation of the physical degrees of freedom of the gravitational field (the tidal effects) from the arbitrary gauge variables. Since a global vision of the equivalence principle implies that only global non-inertial frames can exist in general relativity, the gauge variables are naturally interpreted as generalized relativistic inertial effects, which have to be fixed to get a deterministic evolution in a given non-inertial frame. As a consequence, in each Einstein's space-time in this class the whole chrono-geometrical structure, including also the clock synchronization convention, is dynamically determined and a new approach to the Hole Argument leads to the conclusion that "gravitational field" and "space-time" are two faces of the same entity. This view allows to get a classical scenario for the unification of the four interactions in a scheme suited to the description of the solar system or our galaxy with a deperametrization to special relativity and the subsequent possibility to take the non-relativistic limit.Comment: 33 pages, Lectures given at the 42nd Karpacz Winter School of Theoretical Physics, "Current Mathematical Topics in Gravitation and Cosmology", Ladek, Poland, 6-11 February 200

Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries

The third post-Newtonian approximation to the general relativistic dynamics of two point-mass systems has been recently derived by two independent groups, using different approaches, and different coordinate systems. By explicitly exhibiting the map between the variables used in the two approaches we prove their physical equivalence. Our map allows one to transfer all the known results of the Arnowitt-Deser-Misner (ADM) approach to the harmonic-coordinates one: in particular, it gives the value of the harmonic-coordinates Lagrangian, and the expression of the ten conserved quantities associated to global Poincar\'e invariance.Comment: REVTeX, 13 pages, corrected misprint (wrong sign) in Eq. (4.7), updated reference

Simple-Current Symmetries, Rank-Level Duality, and Linear Skein Relations for Chern-Simons Graphs

A previously proposed two-step algorithm for calculating the expectation values of Chern-Simons graphs fails to determine certain crucial signs. The step which involves calculating tetrahedra by solving certain non- linear equations is repaired by introducing additional linear equations. As a first step towards a new algorithm for general graphs we find useful linear equations for those special graphs which support knots and links. Using the improved set of equations for tetrahedra we examine the symmetries between tetrahedra generated by arbitrary simple currents. Along the way we uncover the classical origin of simple-current charges. The improved skein relations also lead to exact identities between planar tetrahedra in level $K$ $G(N)$ and level $N$ $G(K)$ CS theories, where $G(N)$ denotes a classical group. These results are recast as identities for quantum $6j$-symbols and WZW braid matrices. We obtain the transformation properties of arbitrary graphs and links under simple current symmetries and rank-level duality. For links with knotted components this requires precise control of the braid eigenvalue permutation signs, which we obtain from plethysm and an explicit expression for the (multiplicity free) signs, valid for all compact gauge groups and all fusion products.Comment: 58 pages, BRX-TH-30

Design and enhanced evaluation of a robust anaphor resolution algorithm

Syntactic coindexing restrictions are by now known to be of central importance to practical anaphor resolution approaches. Since, in particular due to structural ambiguity, the assumption of the availability of a unique syntactic reading proves to be unrealistic, robust anaphor resolution relies on techniques to overcome this deficiency. This paper describes the ROSANA approach, which generalizes the verification of coindexing restrictions in order to make it applicable to the deficient syntactic descriptions that are provided by a robust state-of-the-art parser. By a formal evaluation on two corpora that differ with respect to text genre and domain, it is shown that ROSANA achieves high-quality robust coreference resolution. Moreover, by an in-depth analysis, it is proven that the robust implementation of syntactic disjoint reference is nearly optimal. The study reveals that, compared with approaches that rely on shallow preprocessing, the largely nonheuristic disjoint reference algorithmization opens up the possibility/or a slight improvement. Furthermore, it is shown that more significant gains are to be expected elsewhere, particularly from a text-genre-specific choice of preference strategies. The performance study of the ROSANA system crucially rests on an enhanced evaluation methodology for coreference resolution systems, the development of which constitutes the second major contribution o/the paper. As a supplement to the model-theoretic scoring scheme that was developed for the Message Understanding Conference (MUC) evaluations, additional evaluation measures are defined that, on one hand, support the developer of anaphor resolution systems, and, on the other hand, shed light on application aspects of pronoun interpretation

On the origin of ambiguity in efficient communication

This article studies the emergence of ambiguity in communication through the concept of logical irreversibility and within the framework of Shannon's information theory. This leads us to a precise and general expression of the intuition behind Zipf's vocabulary balance in terms of a symmetry equation between the complexities of the coding and the decoding processes that imposes an unavoidable amount of logical uncertainty in natural communication. Accordingly, the emergence of irreversible computations is required if the complexities of the coding and the decoding processes are balanced in a symmetric scenario, which means that the emergence of ambiguous codes is a necessary condition for natural communication to succeed.Comment: 28 pages, 2 figure

On-shell constrained M2M_2 variables with applications to mass measurements and topology disambiguation

We consider a class of on-shell constrained mass variables that are 3+1 dimensional generalizations of the Cambridge $M_{T2}$ variable and that automatically incorporate various assumptions about the underlying event topology. The presence of additional on-shell constraints causes their kinematic distributions to exhibit sharper endpoints than the usual $M_{T2}$ distribution. We study the mathematical properties of these new variables, e.g., the uniqueness of the solution selected by the minimization over the invisible particle 4-momenta. We then use this solution to reconstruct the masses of various particles along the decay chain. We propose several tests for validating the assumed event topology in missing energy events from new physics. The tests are able to determine: 1) whether the decays in the event are two-body or three-body, 2) if the decay is two-body, whether the intermediate resonances in the two decay chains are the same, and 3) the exact sequence in which the visible particles are emitted from each decay chain.Comment: 44pages, 17 figures. revised version, published in JHEP. Minor addition: a paragraph discussing the effect on the background at the end of section 5.

Exact solvability of potentials with spatially dependent effective masses

We discuss the relationship between exact solvability of the Schroedinger equation, due to a spatially dependent mass, and the ordering ambiguity. Some examples show that, even in this case, one can find exact solutions. Furthermore, it is demonstrated that operators with linear dependence on the momentum are nonambiguous.Comment: 12 page

A logic for reasoning about ambiguity

Standard models of multi-agent modal logic do not capture the fact that information is often \emph{ambiguous}, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different semantics that capture different assumptions about the agents' beliefs regarding whether or not there is ambiguity. We examine the expressive power of logics of ambiguity compared to logics that cannot model ambiguity, with respect to the different semantics that we propose.Comment: Some of the material in this paper appeared in preliminary form in "Ambiguous langage and differences of belief" (see arXiv:1203.0699