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1	Quantum models of space-time based on recoupling theory Moussouris, John Peter January 1984 (has links) Models of geometry that are intrinsically quantum-mechanical in nature arise from the recoupling theory of space-time symmetry groups. Roger Penrose constructed such a model from SU(2) recoupling in his theory of spin networks; he showed that spin measurements in a classical limit are necessarily consistent with a three-dimensional Euclidian vector space. T. Regge and G. Ponzano expressed the semi-classical limit of this spin model in a form resembling a path integral of the Einstein-Hilbert action in three Euclidian dimensions. This thesis gives new proofs of the Penrose spin geometry theorem and of the Regge-Ponzano decomposition theorem. We then consider how to generalize these two approaches to other groups that give rise to new models of quantum geometries. In particular, we show how to construct quantum models of four-dimensional relativistic space-time from the re-coupling theory of the Poincare group. 530.1
2	Spinorové techniky pro konstrukci kvazilokálních veličin v obecné relativitě / Spinorial techniques for constructing quasi-local quantities in general relativity Holka, Lukáš January 2014 (has links) No description available.
3	Symmetries of the Point Particle Söderberg, Alexander January 2014 (has links) We study point particles to illustrate the various symmetries such as the Poincaré group and its non-relativistic version. In order to find the Noether charges and the Noether currents, which are conserved under physical symmetries, we study Noether’s theorem. We describe the Pauli-Lubanski spin vector, which is invariant under the Poincaré group and describes the spin of a particle in field theory. By promoting the Pauli-Lubanski spin vector to an operator in the quantized theory we will see that it describes the spin of a particle. Moreover, we find an action for a smooth spinning bosonic particle by compactifying one string dimension together with one embedding dimension. As with the Pauli-Lubanski spin vector, we need to quantize this action to confirm that it is the action for a smooth spinning particle. / Vi studerar punktpartiklar för att illustrera olika symemtrier som t.ex. Poincaré gruppen och dess icke-relativistiska version. För att hitta de Noether laddningar och Noether strömmar, vilka är bevarade under symmetrier, studerar vi Noether’s sats. Vi beskriver Pauli-Lubanksi spin vektorn, vilken har en invarians under Poincaré gruppen och beskriver spin hos en partikel i fältteori. Genom att låta Pauli-Lubanski spin vektorn agera på ett tillstånd i kvantfältteori ser vi att den beskriver spin hos en partikel. Dessutom finner vi en verkan för en spinnande partikel genom att kompaktifiera en bosonisk sträng dimension tillsammans med en inbäddad dimension. Som med Pauli-Lubanski spin vektorn, kvantiserar vi denna verkan för att bekräfta att det är en verkan för en spinnande partikel. symmetries spin classical physics classical field theory action smooth spinning particle pauli-lubanski noether theorem poincare group lorentz group galilean transformations relativistic equations of motion boost rotation translation quantization bosonic string rigid particle momentum momenta generators
4	Field Theoretic Lagrangian From Off-shell Supermultiplet Gauge Quotients Katona, Gregory 01 January 2013 (has links) Recent efforts to classify off-shell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a node-pair transformtion between fermionic bosonic component fields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge-quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or "proper" Adinkras as afore sighted, nor can they be decomposed into supermultiplet sums, but are rather a connected "Adinkraic network". Their iteration, analogous to Weyl's construction for producing all finite-dimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discrete-graph and continuous-field variables, the links of which feature distinct, supersymmetric Lagrangian templates. Collectively, these Adiankraic series air new symbolic genera for equation to phase moments in Feynman path integrals. Guided in this light, we proceed by constructing Lagrangians actions for the N = 3 supermultiplet YI /(iDI X) for I = 1, 2, 3, where YI and X are standard, Salam-Strathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external background (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory responses, some of which are found to be surprisingly controlled by the golden ratio, [phi] = 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 - > 4 supersymmetric extension to the Chiral-Chiral and Chiral-twistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural proiii gression, a continuum of observably and usefully inequivalent, finite-dimensional off-shell representations of worldline N = 4 extended supersymmetry are explored, that are variate from one another but in the value of a tuning parameter, Ref [53]. Their dynamics turns out to be nontrivial already when restricting to just bilinear Lagrangians. In particular, we find a 34-parameter family of bilinear Lagrangians that couple two differently tuned supermultiplets to each other and to external magnetic fluxes, where the explicit parameter dependence is unremovable by any field redefinition and is therefore observable. This offers the evaluation of X-phase sensitive, off-shell path integrals with promising correlations to group product decompositions and to deriving source emergences of higher-order background flux-forms on 2-dimensional manifolds, the stacks of which comprise space-time volumes. Application to nonlinear sigma models would naturally follow, having potential use in M- and F- string theories. Supersymmetry superspace supermultiplet adinkra automata adiankraic tensor product decomposition group theoretic lorentz group su(2) so(3) gauge quotient isomorphism surjective bijective image mapping indefinite adiankraic network sequence super poincare group haag lopuszanski sohnius theorem string theory m theory f theory nonlinear sigma model (numerical) algebraic geometry algebraic paradigms worldsheet worldsheet stacks supersymmetric lagrangians ansatz templates super potentials quantum mechanics field theory fermionic bosonic (super) zeeman background flux fields supergravity superfields young tableaux susy tableaux controlled chaos supercharge continuum chiral chiral twisted chiral Physics

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