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Cambridge, United Kingdom

Anderson E.,DAMTP
Classical and Quantum Gravity

Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1D to include a notion of scale. This is useful as regards forming a tight analogy with quantum cosmology and the emergent semiclassical time and hidden time approaches to the problem of time. This paper shows furthermore that the correspondence between relational particle models and classical and quantum cosmology can be strengthened using judicious choices of the mechanical potential. This gives relational particle mechanics models with analogues of spatial curvature, cosmological constant, dust and radiation terms. A number of these models are then tractable at the quantum level. These models can be used to study important issues (1) in canonical quantum gravity: the problem of time, the semiclassical approach to it and timeless approaches to it (such as the naive Schrödinger interpretation and records theory) and (2) in quantum cosmology, such as in the investigation of uniform states, robustness and the qualitative understanding of the origin of structure formation. © 2011 IOP Publishing Ltd. Source

Anderson E.,DAMTP
Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

I previously showed that Kendall's work on shape geometry is in fact also the geometrical description of Barbour's relational mechanics' reduced configuration spaces (alias shape spaces). I now describe the extent to which Kendall's subsequent statistical application to e.g. the 'standing stones problem' realizes further ideas along the lines of Barbour-type timeless records theories, albeit just at the classical level. © 2015 Elsevier Ltd. Source

Dolan F.A.H.,DAMTP | Spiridonov V.P.,Joint Institute for Nuclear Research | Vartanov G.S.,Max Planck Institute For Gravitationsphysik
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

An exact formula for partition functions in 3. d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific q-hypergeometric integrals whose key building block is the double sine function (or the hyperbolic gamma function). Elliptic hypergeometric integrals, discovered by the second author, define 4. d superconformal indices. Using their reduction to the hyperbolic level, we describe a general scheme of reducing 4. d superconformal indices to 3. d partition functions which imply an efficient way of getting 3. d N=2 supersymmetric dualities for both SYM and CS theories from the "parent" 4. d N=1 dualities for SYM theories. As an example, we consider explicitly the duality pattern for 3. d N=2 SYM and CS theories with SP(2N) gauge group with the antisymmetric tensor matter. © 2011 Elsevier B.V. Source

Mezincescu L.,University of Miami | Routh A.J.,DAMTP | Townsend P.K.,DAMTP
Annals of Physics

In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a "spin-shell" constraint from which the spin content can be read off. We extend this formalism to massive (super)particles (with N-extended space-time supersymmetry) in three and four space-time dimensions, explaining how the spin-shell constraints are related to spin, and we use it to prove equivalence of the massive N = 1 and BPS-saturated N = 2 superparticle actions. We also find the supertwistor form of the action for "spinning particles" with N-extended worldline supersymmetry, massless in four dimensions and massive in three dimensions, and we show how this simplifies special features of the N = 2 case. © 2014. Source

Hartle J.,University of California at Santa Barbara | Hawking S.W.,DAMTP | Hertog T.,University Paris Diderot | Hertog T.,Solvay Group
Physical Review Letters

We consider landscape models that admit several regions where the conditions for eternal inflation hold. It is shown that one can use the no-boundary wave function to calculate small departures from homogeneity within our past light cone despite the possibility of much larger fluctuations on super horizon scales. The dominant contribution comes from the history exiting eternal inflation at the lowest value of the potential. In a class of landscape models this predicts a tensor to scalar ratio of about 10%. In this way the no-boundary wave function defines a measure for the prediction of local cosmological observations. © 2011 American Physical Society. Source

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