Hamiltonian constraint analysis of vector field theories with spontaneous Lorentz symmetry breaking

Recent investigations of various quantum-gravity theories have revealed a variety of possible mechanisms that lead to Lorentz violation. One of the more elegant of these mechanisms is known as Spontaneous Lorentz Symmetry Breaking (SLSB), where a vector or tensor field acquires a nonzero vacuum expectation value. As a consequence of this symmetry breaking, massless Nambu-Goldstone modes appear with properties similar to the photon in Electromagnetism. This thesis considers the most general class of vector field theories that exhibit spontaneous Lorentz violation-known as bumblebee models-and examines their candidacy as potential alternative explanations of E&M, offering the possibility that Einstein-Maxwell theory could emerge as a result of SLSB rather than of local U(1) gauge invariance. With this aim we employ Dirac's Hamiltonian Constraint Analysis procedure to examine the constraint structures and degrees of freedom inherent in three candidate bumblebee models, each with a different potential function, and compare these results to those of Electromagnetism. We find that none of these models share similar constraint structures to that of E&M, and that the number of degrees of freedom for each model exceeds that of Electromagnetism by at least two, pointing to the potential existence of massive modes or propagating ghost modes in the bumblebee theories.

Topologically massive Yang-Mills: A Hamilton-Jacobi constraint analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Programs as paths: An approach to timing constraint analysis

A program can be decomposed into a set of possible execution paths. These can be described in terms of primitives such as assignments, assumptions and coercions, and composition operators such as sequential composition and nondeterministic choice as well as finitely or infinitely iterated sequential composition. Some of these paths cannot possibly be followed (they are dead or infeasible), and they may or may not terminate. Decomposing programs into paths provides a foundation for analyzing properties of programs. Our motivation is timing constraint analysis of real-time programs, but the same techniques can be applied in other areas such as program testing. In general the set of execution paths for a program is infinite. For timing analysis we would like to decompose a program into a finite set of subpaths that covers all possible execution paths, in the sense that we only have to analyze the subpaths in order to determine suitable timing constraints that cover all execution paths.

Electromagnetic field at finite temperature: A first order approach

In this work we study the electromagnetic field at finite temperature via the massless DKP formalism. The constraint analysis is performed and the partition function for the theory is constructed and computed. When it is specialized to the spin 1 sector we obtain the well-known result for the thermodynamic equilibrium of the electromagnetic field. (c) 2006 Elsevier B.V. All rights reserved.

Relativistic particle dynamics in D=2+1

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and tau-reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables lambda(alpha) show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model.

Formalismo de Hamilton-Jacobi à la Carathéodory. Parte 2: sistemas singulares

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Relativistic particle dynamics in D = 2+1

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and τ-reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables λα show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model. © SISSA 2006.

Formalismo de Hamilton-Jacobi generalizado: teorias de campos com derivadas de ordem superior

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

S Q E D (4) and Q E D (4) on the Null-Plane

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

Reliability analysis of transform-based stereo matching techniques, and a new matching constraint

Stereo vision is a method of depth perception, in which depth information is inferred from two (or more) images of a scene, taken from different perspectives. Practical applications for stereo vision include aerial photogrammetry, autonomous vehicle guidance, robotics and industrial automation. The initial motivation behind this work was to produce a stereo vision sensor for mining automation applications. For such applications, the input stereo images would consist of close range scenes of rocks. A fundamental problem faced by matching algorithms is the matching or correspondence problem. This problem involves locating corresponding points or features in two images. For this application, speed, reliability, and the ability to produce a dense depth map are of foremost importance. This work implemented a number of areabased matching algorithms to assess their suitability for this application. Area-based techniques were investigated because of their potential to yield dense depth maps, their amenability to fast hardware implementation, and their suitability to textured scenes such as rocks. In addition, two non-parametric transforms, the rank and census, were also compared. Both the rank and the census transforms were found to result in improved reliability of matching in the presence of radiometric distortion - significant since radiometric distortion is a problem which commonly arises in practice. In addition, they have low computational complexity, making them amenable to fast hardware implementation. Therefore, it was decided that matching algorithms using these transforms would be the subject of the remainder of the thesis. An analytic expression for the process of matching using the rank transform was derived from first principles. This work resulted in a number of important contributions. Firstly, the derivation process resulted in one constraint which must be satisfied for a correct match. This was termed the rank constraint. The theoretical derivation of this constraint is in contrast to the existing matching constraints which have little theoretical basis. Experimental work with actual and contrived stereo pairs has shown that the new constraint is capable of resolving ambiguous matches, thereby improving match reliability. Secondly, a novel matching algorithm incorporating the rank constraint has been proposed. This algorithm was tested using a number of stereo pairs. In all cases, the modified algorithm consistently resulted in an increased proportion of correct matches. Finally, the rank constraint was used to devise a new method for identifying regions of an image where the rank transform, and hence matching, are more susceptible to noise. The rank constraint was also incorporated into a new hybrid matching algorithm, where it was combined a number of other ideas. These included the use of an image pyramid for match prediction, and a method of edge localisation to improve match accuracy in the vicinity of edges. Experimental results obtained from the new algorithm showed that the algorithm is able to remove a large proportion of invalid matches, and improve match accuracy.

A constraint Jacobian based approach for static analysis of pantograph masts

This paper presents a constraint Jacobian matrix based approach to obtain the stiffness matrix of widely used deployable pantograph masts with scissor-like elements (SLE). The stiffness matrix is obtained in symbolic form and the results obtained agree with those obtained with the force and displacement methods available in literature. Additional advantages of this approach are that the mobility of a mast can be evaluated, redundant links and joints in the mast can be identified and practical masts with revolute joints can be analysed. Simulations for a hexagonal mast and an assembly with four hexagonal masts is presented as illustrations.

Exploiting the Structure of the Constraint Graph for Efficient Points-to Analysis

Points-to analysis is a key compiler analysis. Several memory related optimizations use points-to information to improve their effectiveness. Points-to analysis is performed by building a constraint graph of pointer variables and dynamically updating it to propagate more and more points-to information across its subset edges. So far, the structure of the constraint graph has been only trivially exploited for efficient propagation of information, e.g., in identifying cyclic components or to propagate information in topological order. We perform a careful study of its structure and propose a new inclusion-based flow-insensitive context-sensitive points-to analysis algorithm based on the notion of dominant pointers. We also propose a new kind of pointer-equivalence based on dominant pointers which provides significantly more opportunities for reducing the number of pointers tracked during the analysis. Based on this hitherto unexplored form of pointer-equivalence, we develop a new context-sensitive flow-insensitive points-to analysis algorithm which uses incremental dominator update to efficiently compute points-to information. Using a large suite of programs consisting of SPEC 2000 benchmarks and five large open source programs we show that our points-to analysis is 88% faster than BDD-based Lazy Cycle Detection and 2x faster than Deep Propagation. We argue that our approach of detecting dominator-based pointer-equivalence is a key to improve points-to analysis efficiency.

Prioritizing constraint evaluation for efficient points-to analysis

Pervasive use of pointers in large-scale real-world applications continues to make points-to analysis an important optimization-enabler. Rapid growth of software systems demands a scalable pointer analysis algorithm. A typical inclusion-based points-to analysis iteratively evaluates constraints and computes a points-to solution until a fixpoint. In each iteration, (i) points-to information is propagated across directed edges in a constraint graph G and (ii) more edges are added by processing the points-to constraints. We observe that prioritizing the order in which the information is processed within each of the above two steps can lead to efficient execution of the points-to analysis. While earlier work in the literature focuses only on the propagation order, we argue that the other dimension, that is, prioritizing the constraint processing, can lead to even higher improvements on how fast the fixpoint of the points-to algorithm is reached. This becomes especially important as we prove that finding an optimal sequence for processing the points-to constraints is NP-Complete. The prioritization scheme proposed in this paper is general enough to be applied to any of the existing points-to analyses. Using the prioritization framework developed in this paper, we implement prioritized versions of Andersen's analysis, Deep Propagation, Hardekopf and Lin's Lazy Cycle Detection and Bloom Filter based points-to analysis. In each case, we report significant improvements in the analysis times (33%, 47%, 44%, 20% respectively) as well as the memory requirements for a large suite of programs, including SPEC 2000 benchmarks and five large open source programs.

a constraint solver and its application to path feasibility analysis

Many testing methods are based on program paths. A well-known problem with them is that some paths are infeasible. To decide the feasibility of paths, we may solve a set of constraints. In this paper, we describe constraint-based tools that can be used for this purpose. They accept constraints expressed in a natural form, which may involve variables of different types such as integers, Booleans, reals and fixed-size arrays. The constraint solver is an extension of a Boolean satisfiability checker and it makes use of a linear programming package. The solving algorithm is described, and examples are given to illustrate the use of the tools. For many paths in the testing literature, their feasibility can be decided in a reasonable amount of time.