The Corolla Polynomial for spontaneously broken Gauge Theories

In [1, 2, 3] the Corolla Polynomial $\mathcal C (\Gamma) \in \mathbb C [a_{h_1}, \ldots, a_{h_{\left \vert \Gamma^{[1/2]} \right \vert}}]$ was introduced as a graph polynomial in half-edge variables $\left \{ a_h \right \} _{h \in \Gamma^{[1/2]}}$ over a 3-regular scalar quantum field theory (QFT) Feynman graph $\Gamma$. It allows for a covariant quantization of pure Yang-Mills theory without the need for introducing ghost fields, clarifies the relation between quantum gauge theory and scalar QFT with cubic interaction and translates back the problem of renormalizing quantum gauge theory to the problem of renormalizing scalar QFT with cubic interaction (which is super renormalizable in 4 dimensions of spacetime). Furthermore, it is, as we believe, useful for computer calculations. In [4] on which this paper is based the formulation of [1, 2, 3] gets slightly altered in a fashion specialized in the case of the Feynman gauge. It is then formulated as a graph polynomial $\mathcal C ( \Gamma ) \in \mathbb C [a_{h_{1 \pm}}, \ldots, a_{h_{\left \vert \Gamma^{[1/2]} \right \vert} \vphantom{h}_\pm}, b_{h_1}, \ldots, b_{h_{\left \vert \Gamma^{[1/2]} \right \vert}}]$ in three different types of half-edge variables $\left \{ a_{h_+} , a_{h_-} , b_h \right \} _{h \in \Gamma^{[1/2]}}$. This formulation is also suitable for the generalization to the case of spontaneously broken gauge theories (in particular all bosons from the Standard Model), as was first worked out in [4] and gets reviewed here.Comment: 30 pages, 44 figures, article; minor revisions; version to appear in Mathematical Physics, Analysis and Geometr

Gauge Symmetries and Renormalization

The preservation of gauge symmetries to the quantum level induces symmetries between renormalized Green's functions. These symmetries are known by the names of Ward-Takahashi and Slavnov-Taylor identities. On a perturbative level, these symmetries can be implemented as Hopf ideals in the Connes-Kreimer renormalization Hopf algebra. In this article, we generalize the existing literature to the most general case by first motivating these symmetries on a generic level and then proving that they indeed generate Hopf ideals, where we also include the more involved cases of super- and non-renormalizable local QFTs. Finally, we provide a criterion for their validity on the level of renormalized Feynman rules

Algebraic Structures in the Coupling of Gravity to Gauge Theories

This article is an extension of the author's second master thesis [1]. It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry's Theorem. Next, the restricted combinatorial Green's functions for all two-loop propagators and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green's functions necessary for multiplicative renormalization are discussed. Keywords: Quantum Field Theory; Quantum Gravity; Quantum General Relativity; Quantum Electrodynamics; Perturbative Quantization; Hopf Algebraic RenormalizationComment: 57 pages, 259 Feynman diagrams, article; minor revisions; version to appear in Annals of Physic

Why do wages slope upwards? Testing three labor market theories

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Avoiding space robot collisions utilizing the NASA/GSFC tri-mode skin sensor

Sensor based robot motion planning research has primarily focused on mobile robots. Consider, however, the case of a robot manipulator expected to operate autonomously in a dynamic environment where unexpected collisions can occur with many parts of the robot. Only a sensor based system capable of generating collision free paths would be acceptable in such situations. Recently, work in this area has been reported in which a deterministic solution for 2DOF systems has been generated. The arm was sensitized with 'skin' of infra-red sensors. We have proposed a heuristic (potential field based) methodology for redundant robots with large DOF's. The key concepts are solving the path planning problem by cooperating global and local planning modules, the use of complete information from the sensors and partial (but appropriate) information from a world model, representation of objects with hyper-ellipsoids in the world model, and the use of variational planning. We intend to sensitize the robot arm with a 'skin' of capacitive proximity sensors. These sensors were developed at NASA, and are exceptionally suited for the space application. In the first part of the report, we discuss the development and modeling of the capacitive proximity sensor. In the second part we discuss the motion planning algorithm

Material Strength in Polymer Shape Deposition Manufacturing

Shape Deposition Manufacturing (SDM) is a layered manufacturing process involving an iterative combination of material addition and material removal. Polymer SDM processes have used castable thermoset resins to build a variety of parts. The strength of such parts is determined by the bulk material properties of the part materials and by their interlayer adhesion. This paper describes tensile testing of three thermoset resins used for SDM - two polyurethane resins and one epoxy resin. Both monolithic specimens and specimens with two interlayer !nterfaces were tested. Interlayer tensile strengths were found to vary greatly among the three matenals, from 5-40 MPa.Mechanical Engineerin

Spectral rate theory for projected two-state kinetics

Classical rate theories often fail in cases where the observable(s) or order parameter(s) used are poor reaction coordinates or the observed signal is deteriorated by noise, such that no clear separation between reactants and products is possible. Here, we present a general spectral two-state rate theory for ergodic dynamical systems in thermal equilibrium that explicitly takes into account how the system is observed. The theory allows the systematic estimation errors made by standard rate theories to be understood and quantified. We also elucidate the connection of spectral rate theory with the popular Markov state modeling (MSM) approach for molecular simulation studies. An optimal rate estimator is formulated that gives robust and unbiased results even for poor reaction coordinates and can be applied to both computer simulations and single-molecule experiments. No definition of a dividing surface is required. Another result of the theory is a model-free definition of the reaction coordinate quality (RCQ). The RCQ can be bounded from below by the directly computable observation quality (OQ), thus providing a measure allowing the RCQ to be optimized by tuning the experimental setup. Additionally, the respective partial probability distributions can be obtained for the reactant and product states along the observed order parameter, even when these strongly overlap. The effects of both filtering (averaging) and uncorrelated noise are also examined. The approach is demonstrated on numerical examples and experimental single-molecule force probe data of the p5ab RNA hairpin and the apo-myoglobin protein at low pH, here focusing on the case of two-state kinetics

Residual Stresses in Layered Manufacturing

Layered Manufacturing processes accumulate residual stresses during materialbuildup. These stresses may cause part warping and layer delamination. This paper presents work done on investigating residual stress accumulation andp(i,rt distortion of Layered Manufactured artifacts. A simple analyticaLmodel was developed and used to determine how the number of layers and the layer thickness influences part warping. Resllits show that thin layers produce lower part deflection as compared with depositing fewer and thicker layers. In addition to the analytical work, a finite element model wasdeveloped and used to illvestigate the deposition pattern's influence on. the part deflection. Finite element model and corresponding experimental analysis showed that the geometry of the deposition pattern significantly affects the resulting part distortion. This finite element model was also used to investigate an inter-layer surface defect,. known as the Christmas Thee Step, that is associated with Shape Deposition Manufacturing. Results indicate that the features of this defect are influenced only by the material deposited close. to the part·surface and the particular material deposited. The step is not affected by the deposition pattern.Mechanical Engineerin