| 1. |
- Barros e Sá, Nuno Baltazar Fogaça
(författare)
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Studies in general relativity and quantum mechanics
- 2000
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This work approaches two different subjects in theoretical Physics: General relativity, and the geometry of the space of quantum states.Concerning the former subject we review the Lagrangian and Hamiltonian formulations of General relatvity with particular emphasis on its description by means of tetrads and connections, either real or complex self-dual. We include the Lagrangian analysis of matter fields and compare the metric and connection minimally coupled theories. We also consider the real connection description of Gravity obtained after partial gauge-fixing, where we make an effort to understand the role played in the theory by the free parameter involved in the definition of the new variables. And we study the limit of the connection formalism when the gravitational constant goes to zero, and other diffeomorphism invariant theories with no local degrees of freedom for the geometrical variables, such as parameterized field theory.Concerning the latter subject we study the decompostion of projective Hilbert space in orbits fo the group generating sets of coherent states. We analyze the orbit spaces in spin systems and in particle mechanics, and the construciton of functions in Hilbert space which are invariant under the action of the group. We finish by discussing the concept of uncertainty in spin systems.
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| 2. |
- Henneaux, Marc, et al.
(författare)
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Coxeter group structure of cosmological billiards on compact spatial manifolds
- 2008
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Ingår i: Journal of High Energy Physics. - : Springer Science and Business Media LLC. - 1029-8479 .- 1126-6708. ; 2008:9, s. 49-
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Tidskriftsartikel (refereegranskat)abstract
- We present a systematic study of the cosmological billiard structures of Einstein-p-form systems in which all spatial directions are compactified on a manifold of nontrivial topology. This is achieved for all maximally oxidised theories associated with split real forms, for all possible compactifications as defined by the de Rham cohomology of the internal manifold. In each case, we study the Coxeter group that controls the dynamics for energy scales below the Planck scale as well as the relevant billiard region. We compare and contrast them with the Weyl group and fundamental domain that emerge from the general BKL analysis. For generic topologies we find a variety of possibilities: ( i) The group may or may not be a simplex Coxeter group; ( ii) The billiard region may or may not be a fundamental domain. When it is not a fundamental domain, it can be described as a sequence of pairwise adjacent chambers, known as a gallery, and the reflections in the billiard walls provide a non-standard presentation of the Coxeter group. We find that it is only when the Coxeter group is a simplex Coxeter group, and the billiard region is a fundamental domain, that there is a correspondence between billiard walls and simple roots of a Kac-Moody algebra, as in the general BKL analysis. For each compactification we also determine whether or not the resulting theory exhibits chaotic dynamics.
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| 3. |
- Palmkvist, Jakob, 1980
(författare)
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Exceptional Lie algebras and M-theory
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study algebraic structures in M-theory, in particular the exceptional Lie algebras arising in dimensional reduction of its low energy limit, eleven-dimensional supergravity. We focus on e8 and its infinite-dimensional extensions e9 and e10. We review the dynamical equivalence, up to truncations on both sides, between eleven-dimensional supergravity and a geodesic sigma model based on the coset E10/K(E10), where K(E10) is the maximal compact subgroup. The description of e10 as a graded Lie algebra is crucial for this equivalence. We study generalized Jordan triple systems, which are closely related to graded Lie algebras, and which may also play a role in the description of M2-branes using three-dimensional superconformal theories. The introductory part is followed by five research papers.In Paper I we show that the spinor and vector-spinor representations of k(e10) in the fermionic extension of the original E10 coset model lead, upon restriction to k(e9), to the R-symmetry transformations in eleven-dimensional supergravity reduced to two dimensions. Paper II provides an explicit expression for the primitive E8 invariant tensor with eight symmetric indices, which is expected to appear in M-theory corrections in the reduction to three dimensions. In Paper III we show that e8, e9 and e10 can be constructed in a unified way from a Jordan algebra, via generalized Jordan triple systems. Also Paper IV deals with generalized Jordan triple systems, but in the context of superconformal M2-branes. We show that the recently proposed theories with six or eight supersymmetries can be expressed in terms of a graded Lie algebra. In Paper V we return to the bosonic E10 coset model, and apply it to gauged maximal supergravity in three dimensions.
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| 4. |
- Persson, Daniel, 1978, et al.
(författare)
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Massive Type IIA Supergravity and E10
- 2009
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Ingår i: Fortschritte der Physik. - : Wiley. - 0015-8208 .- 1521-3978. ; 57:5-7, s. 580-586
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Tidskriftsartikel (refereegranskat)abstract
- In this talk we investigate the symmetry under E10 of Romans' massive type IIA supergravity. We show that the dynamics of a spinning particle in a non-linear sigma model on the coset space E10/K(E10) reproduces the bosonic and fermionic dynamics of massive IIA supergravity, in the standard truncation. In particular, we identify Romans' mass with a generator of E10 that is beyond the realm of the generators of E10 considered in the eleven-dimensional analysis, but using the same, underformed sigma model. As a consequence, this work provides a dynamical unification of the massless and massive versions of type IIA supergravity inside E10.
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| 5. |
- Persson, Daniel, 1978, et al.
(författare)
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On the E10/Massive Type IIA Supergravity Correspondence
- 2009
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Ingår i: Physical Review D - Particles, Fields, Gravitation and Cosmology. - 2470-0010 .- 2470-0029. ; 79:4, s. 045088-
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we investigate in detail the correspondence between E10 and Romans' massive deformation of type IIA supergravity. We analyse the dynamics of a non-linear sigma model for a spinning particle on the coset space E10/K(E10) and show that it reproduces the dynamics of the bosonic as well as the fermionic sector of the massive IIA theory, within the standard truncation. The mass deformation parameter corresponds to a generator of E10 outside the realm of the generators entering the usual D=11 analysis, and is naturally included without any deformation of the coset model for E10/K(E10). Our analysis thus provides a dynamical unification of the massless and massive versions of type IIA supergravity inside E10. We discuss a number of additional and general features of relevance in the analysis of any deformed supergravity in the correspondence to Kac-Moody algebras, including recently studied deformations where the trombone symmetry is gauged.
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