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

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

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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Financial Power and Democratic Legitimacy

To what extent are questions of sovereign debt a matter for political rather than scientific or moral adjudication? We answer that question by defending three claims. We argue that (i) moral and technocratic takes on sovereign debt tend to be ideological in a pejorative sense of the term, and that therefore (ii) sovereign debt should be politicised all the way down. We then show that this sort of politicisation need not boil down to the crude Realpolitik of debtor-creditor power relations—a conclusion that would leave no room for normative theory, among other problems. Rather, we argue that (iii) in a democratic context, a realist approach to politics centred on what Bernard Williams calls ‘The Basic Legitimation Demand’ affords a deliberative approach to the normative evaluation of public debt policy options

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

The usefulness of a Happy Income Index

In this paper, Happy Income is introduced as an indicator of physical and socio-psychic wellbeing. It is constructed on the assumption that socio-economic well-being is based on objective circumstances, such as personal income as well as on a subjective evaluation of life. In combining these factors, Happy Income is a cardinal measure of overall well-being in a given country. Therefore, Happy Income is not subject to the limitations of purely ordinally scaled indicators, i.e. it is not restricted by an upper bound, which may be one explanation of the Easterlin paradox. The Happy Income concept is employed to measure social well-being in various different European countries. The results are compared to these countries' score on Ruut Veenhoven's Happy Life Years. It is argued that Happy Income is a valuable complement to other indicators of well-being at an aggregated level. --Happiness research,Happy Income,Happy Life Years,Subjective Well-being