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Special geometry of euclidean supersymmetry I: vector multiplets
 J. High Energy Phys
"... Abstract: We construct two new versions of the cmap which allow us to obtain the target manifolds of hypermultiplets in Euclidean theories with rigid N = 2 supersymmetry. While the Minkowskian paracmap is obtained by dimensional reduction of the Minkowskian vector multiplet lagrangian over time, ..."
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Abstract: We construct two new versions of the cmap which allow us to obtain the target manifolds of hypermultiplets in Euclidean theories with rigid N = 2 supersymmetry. While the Minkowskian paracmap is obtained by dimensional reduction of the Minkowskian vector multiplet lagrangian over time, the Euclidean paracmap corresponds to the dimensional reduction of the Euclidean vector multiplet lagrangian. In both cases the resulting hypermultiplet target spaces are parahyperKähler manifolds. We review and prove the relevant results of paracomplex and parahypercomplex geometry. In particular, we give a second, purely geometrical construction of both cmaps, by proving that
Loop quantum gravity: An outside view
, 2005
"... We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the offshell (‘strong’) closure of the constraint algebra is a crucial test of quantum spacetime covariance, and thereby of th ..."
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We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the offshell (‘strong’) closure of the constraint algebra is a crucial test of quantum spacetime covariance, and thereby of the consistency, of the theory. Special attention is paid to the appearance of a large number of ambiguities, in particular in the formulation of the Hamiltonian constraint. Developing suitable approximation methods to establish a connection with classical gravity on the one hand, and with the physics of elementary particles on the other, remains a major challenge. Contents 1 Key questions 2
Coordinates, observables and symmetry in relativity
, 2009
"... We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a “pointcoincidence ” between ..."
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We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a “pointcoincidence ” between scalar fields that completely characterise a spacetime model, we also propose a natural generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all pointcoincidences forms in generic situations a fourdimensional manifold, which is naturally identified with the physical spacetime.
The Search for Quantum Gravity Signals
, 2005
"... We give an overview of ongoing searches for effects motivated by the study of the quantumgravity problem. We describe in greater detail approaches which have not been covered in recent “Quantum Gravity Phenomenology ” reviews. In particular, we outline a new framework for describing Lorentz invarian ..."
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We give an overview of ongoing searches for effects motivated by the study of the quantumgravity problem. We describe in greater detail approaches which have not been covered in recent “Quantum Gravity Phenomenology ” reviews. In particular, we outline a new framework for describing Lorentz invariance violation in the Maxwell sector. We also discuss the general strategy on the experimental side as well as on the theoretical side for a search for quantum gravity effects. The role of test theories, kinematical and dymamical, in this general context is emphasized. The present status of controlled laboratory experiments is described, and we also summarize some key results obtained on the basis of astrophysical observations. 1 Introduction and preliminary remarks 1.1 The search for quantum gravity Our present description of the laws of physics may be characterized as obtained from two types of constituents. The first type of constituent are theoretical frameworks which apply to all physical phenomena at any instant. These “universal ” or “frame ” theories are Quantum Theory (all matter
Problem of time in quantum gravity
 Ann. Phys. (Berlin
, 2012
"... The Problem of Time occurs because the ‘time ’ of GR and of ordinary Quantum Theory are mutually incompatible notions. This is problematic in trying to replace these two branches of physics with a single framework in situations in which the conditions of both apply, e.g. in black holes or in the ver ..."
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The Problem of Time occurs because the ‘time ’ of GR and of ordinary Quantum Theory are mutually incompatible notions. This is problematic in trying to replace these two branches of physics with a single framework in situations in which the conditions of both apply, e.g. in black holes or in the very early universe. Emphasis in this Review is on the Problem of Time being multifaceted and on the nature of each of the eight principal facets. Namely, the Frozen Formalism Problem,
Emergent Quantum Mechanics as a Thermal Ensemble, arXiv:1304.6295 [mathph
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ON THE RECOVERY OF GEOMETRODYNAMICS FROM TWO DIFFERENT SETS OF FIRST PRINCIPLES
, 2006
"... The conventional spacetime formulation of general relativity may be recast as a dynamics of spatial 3geometries (geometrodynamics). Furthermore, geometrodynamics can be derived from first principles. I investigate two distinct sets of these: (i) Hojman, Kuchaˇr and Teitelboim’s, which presuppose th ..."
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The conventional spacetime formulation of general relativity may be recast as a dynamics of spatial 3geometries (geometrodynamics). Furthermore, geometrodynamics can be derived from first principles. I investigate two distinct sets of these: (i) Hojman, Kuchaˇr and Teitelboim’s, which presuppose that the spatial 3geometries are embedded in spacetime. (ii) The 3space approach of Barbour, Foster, Ó Murchadha and Anderson in which the spatial 3geometries are presupposed but spacetime is not. I consider how the constituent postulates of the conventional approach to relativity emerge or are to be built into these formulations. I argue that the 3space approach is a viable description of classical physics (fundamental matter fields included), and one which affords considerable philosophical insight because of its ‘relationalist’ character. From these assumptions of less structure, it is also interesting that conventional relativity can be recovered (albeit as one of several options). However, contrary to speculation in the earlier 3space approach papers, I also argue that this approach is not selective over which sorts of fundamental matter physics it admits. In particular, it does not imply the equivalence principle.
Symmetries, singularities and the deemergence of space
 International Journal of Modern Physics D
, 2008
"... Abstract: Recent work has revealed intriguing connections between a BelinskyKhalatnikovLifshitztype analysis of spacelike singularities in General Relativity and certain infinite dimensional Lie algebras, and in particular the ‘maximally extended ’ hyperbolic Kac–Moody algebra E10. In this essay ..."
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Abstract: Recent work has revealed intriguing connections between a BelinskyKhalatnikovLifshitztype analysis of spacelike singularities in General Relativity and certain infinite dimensional Lie algebras, and in particular the ‘maximally extended ’ hyperbolic Kac–Moody algebra E10. In this essay we argue that these results may lead to an entirely new understanding of the (quantum) nature of space(time) at the Planck scale, and hence – via an effective ‘deemergence ’ of space near a singularity – to a novel mechanism for achieving background independence in quantum gravity. 1. Introduction. A
Minisuperspace Model of Machian Resolution of Problem of Time. II. Bianchi IX", forthcoming
"... A local resolution to the Problem of Time that is Machian and was previously demonstrated for relational mechanics models is here shown to work for a more widely studied quantum cosmological model. I.e., closed isotropic minisuperspace GR with minimallycoupled scalar field matter. This resolution u ..."
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A local resolution to the Problem of Time that is Machian and was previously demonstrated for relational mechanics models is here shown to work for a more widely studied quantum cosmological model. I.e., closed isotropic minisuperspace GR with minimallycoupled scalar field matter. This resolution uses work firstly along the lines of Barbour’s at the classical level. Secondly, it uses a Machianized version of the Semiclassical Approach to Quantum Cosmology (the resolution given is not more than semiclassical). Finally, it uses a Machianized version of a combined Semiclassical Histories Timeless Records scheme along the lines of Halliwell’s work. This program’s goal is the treatment of inhomogeneous perturbations about the present paper’s model. This draws both from this paper’s minisuperspace work and from qualitative parallels with relational particle mechanics, since both have nontrivial notions of inhomogeneity/structure (clumping) as well as nontrivial linear constraints. PACS 04.60Kz