Scientific Series

We present a quantization method based on theEhrenfest theorem embedded in an extended algebraic structure capableof consistently describing hybrid quantum-classical systems, where thestandard quantum and classical mechanics are two limiting cases. TheWigner phase space formulation and the Schordinger equation are foundto be two alternative representations of the quantum case while theKoopman-von Neumann equation is the corresponding classicalcounterpart. Moreover, the developed quantization procedure isgeneralized to describe open systems, quantum/classical field theoriesand relativistic mechanics where new dynamical equations appear,shedding new light on important practical problems such asunderstanding of the quantum/classical transition and modeling ofmesoscopic systems.

Related references: arXiv:1105.4014, arXiv:1112.3679, arXiv:1107.5139

We evaluate the partition function of three dimensional general relativity with a negative cosmological constant, including all known perturbative and non-perturbative contributions to the sum over geometries.

In this talk, I am going to test the concordance cosmology in three different cosmic scales. (1) On the super-horizon scale, “Copi etal. (2009)” have been arguing that the lack of large angular correlations of the CMB temperature field provides strong evidence against the standard, statistically isotropic, LCDM cosmology. I am going to argue that the “ad-hoc” discrepancy is due to the sub-optimal estimator of the low-l multipoles, and a posteriori statistics, which exaggerates the statistical significance. (2) LCDM model also predict the existence of primordial gravitational wave, for which B-mode polarization will be a powerful tool to distinguish different models of the early Universe; (3) On Galactic scales, “Watkins et al. (2008)” shows that the very large bulk flow prefers a very large density fluctuation, which seems to contradict to the LCDM model. We provide a physical explanation for this big bulk flow, based on the assumption that CMB frame does not coincide with matter rest frame, resulting in the tilted Universe. We show that the ‘tilted Universe’ could well explain the bulk flow phenomena and more importantly, the constraints for this tilted Universe can lead to the constraint on the number of e-folds of inflation; (4) In addition, cosmic Mach Number from peculiar velocity catalog may provide a powerful test of the growth of the structure.

I will introduce models of dynamical electroweak symmetry breaking and their present and future impact on LHC physics. I will start by reviewing what LHC has seen and not seen and the main challenges of models of dynamical electroweak symmetry breaking. To overcome some of these problems we need a better understanding of strong dynamics. I will therefore review the state-of-the-art of the phase diagram of strongly coupled theories as function of the number of flavors, colors and matter representation. I will then show how these models can also lead to natural dark matter candidates able to provide a simple resolution to current experimental observations. If times allows, I will introduce new successful models of inflation in which the inflaton emerges as a composite state from a natural four-dimensional strongly coupled theory coupled to gravity.

Categorical quantum mechanics (CQM) uses symmetric monoidal categories to formalize quantum theory, in order to extract the key structures that yield protocols such as teleportation in an abstract way. This formalism admits a purely graphical calculus, but the causal structure of these diagrams, and the formalism in general, is unclear. We begin by considering the signaling abilities of probabilistic devices with inputs and outputs and we show how a non-signaling device can become a perfect signaling device under time-reversal. This conflicts with the causal structure of relativity, and suggests that an `asymmetry' is needed when formalizing causality in CQM. We then show how a fixed causal structure within CQM corresponds to topological connectedness in the graphical language, and that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of a global state forces the monoidal product to be only partially defined, which in turn results in a covariance theorem. These structural results lead to a mathematical entity which we call a `causal category'.

I will first present a theorem based on the Decoupling Theorem of [1] which gives sufficient and necessary conditions for a quantum channel (CPTPM) being such that it yields the same output for almost all possible inputs. This theorem allows us to reproduce and generalize results oft [2,3], in which cornerstones of statistical physics are derived from first principles of quantum mechanics, in a very natural and easy way. Specifically, we express them in a way which allows to apply results about random 2-qubit interactions [4]. Furthermore, we apply this theorem to provide a criterion for whether different initial states of some subspace of a quantum mechanical system in contact with an environment have at some given time already evolved to the same state or not. As it turns out, this question can be answered by examining a simple entropic inequality evaluated for just one particular state [5]. Applying this criterion to realistic Hamiltonians with local interactions may lead to improved bounds on the thermalization times of quantum mechanical systems.

Quantum gravity is about finding out what is the more fundamental nature of spacetime, as a physical system. Several approaches to quantum gravity, suggest that the very description of spacetime as a continuum fails at shorter distances and higher energies, and should be replaced by one in terms of discrete, pre-geometric degrees of freedom, possibly of combinatorial and algebraic nature.

I will present a new approach to information theoretic foundations of quantum theory, developed in order to encompass quantum field theory and curved space-times. Its kinematics is based on the geometry of spaces of integrals on W*-algebras, and is independent of probability theory and Hilbert spaces. It allows to recover ordinary quantum mechanical kinematics as well as emergent curved space-times. Unlike the approaches based on lattices of projections, this kinematics provides a direct mathematical generalisation of the ordinary probability theory to the regime of non-commutative algebras. The new quantum information dynamics is provided by the constrained maximisation of quantum relative entropy. The von Neumann-Lueders rule and several other rules of that type, including Bayes' rule in commutative case, are the special cases of it. Using Favretti's generalisation of the Jaynes-Mitchell source theory, I will show how this dynamics allows one to derive `interacting QFT'-like correlation functions and perturbation expansions in geometric terms of experimental control-and-response parameters, without using Hilbert spaces or measure spaces. Finally, I will present a new bayesian interpretation of quantum theory, aimed at dealing with the intersubjective experimental verifiability, but without providing any ontological claims. Quite noticeably, this interpretation leads to a concrete category theoretic formulation of the new foundations.

I will present a newly found duality between an infinite class of 3-dimensional N=4 gauge theories at their conformal IR fixed point and type IIB string theory solutions. This correspondence gives a new tool to explore the strongly coupled phase of the supersymmetric gauge theories in question.