The theory of quantum electrodynamics is recognized for the most accurate predictions in physics confirmed by experiment. I review the recent results on high precision tests of QED with an emphasize on the study of the positronium bound state.
There has been renewed interest in the effect that pre and postselection has on the foundations of quantum theory. Often, but not solely, in conjunction with weak measurement, pre and postselection scenarios are said to simultaneous create and resolve paradoxes. These paradoxes are said to be profound quandaries which bring us closer to the resolving the mysteries of the quantum. Here I was show that the same effects are present in classical physics when postselection and disturbance are allowed. In particular, I will demonstrate that anomalous weak values and protective measurements are already present in classical theory, thereby showing that these effects do not represent something uniquely quantum nor something that ought to be thought of as paradoxical. This is joint work with Josh Combes and Matt Leifer.
We prove that the $\lambda\phi^4_4$ quantum field theory on noncommutative Moyal space is, in the limit of infinite noncommutativity, exactly solvable in terms of the solution of a non-linear integral equation. The proof involves matrix model techniques which might be relevant for 2D quantum gravity and its generalisation to coloured tensor models of rank $\geq 3$. Surprisingly, our limit describes Schwinger functions of a Euclidean quantum field theory on standard $\mathbb{R}^4$ which satisfy the easy Osterwalder-Schrader axioms boundedness, covariance and symmetry. We prove that the decisive reflection positivity axiom is, for the 2-point function, equivalent to the question whether or not the solution of the integral equation is a Stieltjes function. The numerical solution of the integral equation leaves no doubt that this is true for coupling constants $\lambda\in[-0.39,0]$.
We relate CMB anomalies and the recent observational evidence of primordial gravitational waves. Two aspects are investigated:
(a) Several anomalies are spotted on the low ell temperature map of the WMAP and Planck experiments. However, those anomalies disappear at high ell. We propose that those low ell temperature anomalies may come from nearly scale invariant anomalies of the tensor sector. Those anomalies on the temperature map naturally decay towards small scales, characterized by the tensor-to-temperature radiation transfer function.
(b) The anomalies introduced by the gravitational waves discovery. Strong tension is noticed between the BICEP2 and Planck data. We study in detail how blue tilt of the tensor spectrum reconciles the tension between those datasets.
We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate space of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector. We also show that local reconstruction is possible for thermal states of local Hamiltonians. Finally, we discuss a procedure to certify that the reconstructed state is close to the true global state. We call the entropy of our reconstructed maximum entropy state the "reconstruction entropy", and we discuss its relation to emergent geometry in the context of holographic duality. This is a joint work with Brian Swingle.
The talk is based on joint work with Yuri Manin (arXiv:1402.2158). Using algebro-geometric blowups it is possible to construct a family of models of gluing of aeons across a Big-Bang type singularity, which includes the case of Penrose's conformally cyclic cosmology, as well as inflationary multiverse models generalizing the "eternal symmetree", and BKLL mixmaster type cosmologies. Using the mixmaster dynamics, formulated in terms of elliptic curves and modular curves, we speculate on the geometry of cosmological time near the gluing of aeons. We show also that this type of model allows for phenomena of noncommutativity of spacetime coordinates near the Big-Bang and the crossing of aeons.
Accreting supermassive black holes in the centres of galaxies (i.e. Active Galactic Nuclei - AGN) are now known to play a prominent role in the growth of galaxies through cosmic time. The fundamental parameters to explain the whole range of observed properties of these accreting systems, however, is still elusive. We will present some results from multi-wavelength investigations of the nature of accreting supermassive black holes, including those that produce low kinetic power jets as well as high kinetic power, relativistic jets.
The authors have revealed a fundamental structure which has been hidden within the Wheeler-DeWitt (WDW) constraint of four dimensional General Relativity (GR) of Lorentzian signature in the Ashtekar self-dual variables. The WDW equation can be written as the commutator of two geometric entities, namely the imaginary part of the Chern-Simons functional Q and the local volume element V(x) of 3-space. Upon quantization with cosmological constant, the WDW equation takes on the form of the Lie algebra of the affine group of transformations of the straight line, with Q and V(x) playing the role of the generators for the Lie algebra. The generators are Hermitian, which addresses the issue of the implementation of the reality conditions of GR at the quantum level. Additionally, the irreducible unitary representations (IUR) implement the positivity of the spectrum of the volume operator V(x) at the quantum level This development has led to the existence of elements of the physical Hilbert space for four dimensional gravity of Lorentzian signature, the full theory, in the form of irreducible, unitary representations of the affine group of transformations of the straight line. The affine Lie algebraic structure of the WDW equation remains intact even in the presence of nongravitational fields. This feature has led to the extension of the affine group formulation to elements of the physical Hilbert space for gravity coupled to the full Standard Model of particle physics, quantized on equal footing. Work on the physical interpretation of the states with respect to gauge-diffeomorphism invariant observables, and spacetime geometries solving the Einstein equations is in progress. The journal reference for these results are as follows: - The first result has been published in CQG 30 (2013) 065013 - The second result has just been published in Annals of Physics Journal Vol.343, pages 153-163, April 2014
We show that in the presence of a chemical potential, black hole evaporation generates baryon number. If the inflaton or Ricci scalar is derivatively coupled to the B-L current, the expansion of the universe acts as a chemical potential and splits the energy levels of particles and their anti-particles. The asymmetric Hawking radiation of primordial black holes can thus be used to generate a B-L asymmetry. If dark matter is produced by the same mechanism, the coincidence between the mass density of visible and dark matter can be naturally explained.
The circuit-to-Hamiltonian construction translates a dynamics (a quantum circuit and its output) into statics (the groundstate of a circuit Hamiltonian) by explicitly defining a quantum register for a clock. The standard Feynman-Kitaev construction uses one global clock for all qubits while we consider a different construction in which a clock is assigned to each point in space where a qubit of the quantum circuit resides. We show how one can apply this construction to one-dimensional quantum circuits for which the circuit Hamiltonian realizes the dynamics of a vibrating string. We discuss how the construction can be used (1) in quantum complexity theory to obtain new and stronger results in QMA and (2) how one can realize, based on this construction, universal quantum adiabatic computation and a universal quantum walk using a 2D interacting particle Hamiltonian. See http://arxiv.org/abs/1311.6101