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Topological order is a new kind of collective order which appears in two-dimensional quantum systems such as the fractional quantum Hall effect and brings about rather unusual particles: unlike bosons or fermions these anyons obey exotic statistics and can be exploited to perform quantum computation. Topological order also implies that quantum states at low energies exhibit a very subtle, yet intricate inner structure. Remarkably, both phenomena can be studied in relatively simple spin systems (like Kitaev's quantum double models and the ubiquitous toric code) which in fact capture the essential properties of entire topological phases of matter in many important cases. What is the relationship between these topological phases? Reviewing recent work I will explain how they arrange themselves in a landscape of dualities and hierarchies. In particular, I will focus on two aspects: first, a duality between electric and magnetic quasiparticles in generalized quantum double models and second, a hierarchy construction of quantum states which are related by the condensation of topological charges.

Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. But what is their physical origin? In this talk, I show how it is possible to trace the complex nature of the quantum formalism directly to the basic symmetries associated with the basic operations which allow elementary experiments to be combined into more elaborate ones. In particular, I show that, by harnessing these symmetries, the Feynman rules of quantum theory can be derived from the assumption that a pair of real numbers is associated to each sequence of measurement outcomes, and that the probability of this sequence is a real-valued function of this number pair. The derivation has numerous intriguing implications, such as pointing to a deep connection between the foundations of quantum theory and the foundations of number systems. It also demonstrates that, contrary to the rather prevalent working hypothesis that the structure of the quantum formalism has something essentially to do with nonlocality, the core of the quantum formalism in fact does not depend in any essential way on the properties of space. Reference: "Origin of Complex Quantum Amplitudes and Feynman's Rules", Phys. Rev. A 81, 022109 (2010). Full text available at www.philipgoyal.org

Peter Evans The extent to which Julian Barbour's Machian formulation of general relativity and his interpretation of canonical quantum gravity can be called timeless is addressed. We differentiate two types of timelessness in Barbour's work (1994a, 1994b and 1999) and attempt to refine Barbour's metaphysical claim by providing an account of the essential features of time through considerations of the representation of time in physical theory. We argue that Barbour's claim of timelessness is dubious with respect to his Machian formulation of general relativity but warranted with respect to his interpretation of canonical quantum gravity. We conclude by discussing some of the implications of Barbour's view.

The aim of this talk is to review and discuss some aspects of quantum entanglement in the quantum field theoretic (QFT) domain. The discussion takes place in the algebraic approach to QFT, the motivation for which is briefly discussed. We consider in what sense this approach is sometimes called 'local quantum theory'. We discuss a possible 'realist' understanding of quantum entanglement within this framework, addressing some conceptual and methodological worries raised by Einstein (among others).

The de Broglie-Bohm pilot-wave program is an attempt to formulate quantum theory (including quantum field theory) as a theory without observers, by assuming that the wave-function is not the complete description of a system, but must be supplemented by additional variables (beables). Although many progress has been made in order to extend the pilot-wave theory to quantum field theory, a compelling ontology for quantum field theory is still lacking and the choice of beable is likely to be relevant for the study of quantum non-equilibrium systems and their relaxation properties (Valentini). The present work takes its root in the fact that in the standard model of particle physics, all fermions are fundamentally massless and acquire their bare mass when the Higgs field condenses. In our tentative to build a pilot-wave model for quantum field theory in which beables are attributed to massless fermions, we are naturally led to Weyl spinors and to Penrose's zig-zag picture of the electron. In my talk, I will sketch this tentative and insist on some of its remarkable properties: namely that a positive-energy massive Dirac electron can be thought of as a superposition of positive and negative energy Weyl spinors of the same helicity, and that the massive Dirac electron can in principle move luminally at all times. Based on a joint work with H. Wiseman.