Scientific Series

The purpose of this talk is to describe bosonic fields and their Lagrangians in the causal set context. Spin-0 fields are defined to be real-valued functions on a causal set. Gauge fields are viewed as SU(n)-valued functions on the set of pairs of elements of a causal set, and gravity is viewed as the causal relation itself. The purpose of this talk is to come up with expressions for the Lagrangian densities of these fields in such a way that they approximate the Lagrangian densities expected from regular Quantum Field Theory on a differentiable manifold in the special case where the causal set is a random sprinkling of points in the manifold. I will then conjecture that that same expression is appropriate for an arbitrary causal set.

The consequences of a modified gravity (MOG) are explored. I demonstrate how the solutions of the field equations obtained from the action principle of the MOG lead to a theory without any free, adjustable parameters or ad-hoc empirical formulae. The theory successfully explains solar system observations, the dispersion velocities of globular clusters, the rotation curves of galaxies, the mass profiles of X-ray clusters, the dispersion velocities of satellite galaxies, the Bullet Cluster and cosmological observations without exotic dark matter. The peculiar features of the recent data obtained for the merging cluster Abell 520 are discussed. MOG predicts agreement with data from the scale of the solar system to cosmological scales without dark matter. With no undetermined free parameters, the theory can be used to make firm predictions that may be verifiable in the foreseeable future.

We consider the large N limit of a class of fourdimensional supersymmetric theories in conjunction with a limit in their parameter space towards singular points where extra baryonic states become light, which causes the low-energy description to break down. However, this can be cured by defining a large N double scaling limit where one approaches the singularity by keeping the mass M of these states fixed. This limit has several interesting features. For example, the conventional \\\'t Hooft limit leads to a free theory of colour singlet states where all interactions are suppressed by powers of 1/N. In this case, the large N Hilbert space splits into two decoupled sectors, and one of them keeps residual interactions whose strength in inversely proportional to the mass M. We argue that for a class of these models the dynamics of this sector is dual to a non-critical superstring background, which is exactly solvable.

The principles of Quantum Mechanics and of Classical General Relativity imply Uncertainty Relations between the different spacetime coordinates of the events, which yield to a basic model of Quantum Minkowski Space, having the full (classical) Poincare\' group as group of symmetries. The four dimensional Euclidean distance is a positive operator bounded below by a constant of order one in Planck units; the area operator and the four volume operator are normal operators - the latter being a Lorentz invariant operator with pure point spectrum - whose moduli are also bounded below by a constant of order one. While the spectrum of the 3 volume operator includes zero. These findings are in perfect agreement with the physical intuition suggested by the Spacetime Uncertainty Relations which are implemented by the Algebra of Quantum Spacetime. The formulations of interactions between quantum fields on Quantum Spacetime will be discussed. The various approaches to interactions, equivalent to one another on the Minkowski background, yield to different schemes on Quantum Spacetime, with the common feature of a breakdown of Lorentz invariance due to interactions. In particular one of these schemes will be discussed and motivated, which leads to fully Ultraviolet-Finite theories. Quantum fields will depend on the quantum coordinates, but, in presence of Gravity, the commutators of the coordinates might in turn depend on the quantum fields, giving rise to a quantum texture where fields and spacetime coordinates cannot be separated. Possible deep physical consequences will be outlined.

I should like to show how particular mathematical properties can limit our metaphysical choices, by discussing old and new theorems within the statistical-model framework of Mielnik, Foulis & Randall, and Holevo, and what these theorems have to say about possible metaphysical models of quantum mechanics. Time permitting, I should also like to show how metaphysical assumptions lead to particular mathematical choices, by discussing how the assumption of space as a relational concept leads to a not widely known frame-invariant formulation of classical point-particle mechanics by Föppl and Zanstra, and related research topics in continuum mechanics and general relativity.

A convergence of climate, resource, technological, and economic stresses gravely threaten the future of humankind. Scientists have a special role in humankind\\\'s response, because only rigorous science can help us understand the complexities and potential consequences of these stresses. Diminishing the threat they pose will require profound social, institutional, and technological changes -- changes that will be opposed by powerful status-quo special interests. Do scientists have a responsibility to articulate the dangers of inaction to a broader event beyond simply publishing their findings in scholarly journals? Should they become more actively involved in the politics of global change?

Mutually unbiased bases (MUBs) have attracted a lot of attention the last years. These bases are interesting for their potential use within quantum information processing and when trying to understand quantum state space. A central question is if there exists complete sets of N+1 MUBs in N-dimensional Hilbert space, as these are desired for quantum state tomography. Despite a lot of effort they are only known in prime power dimensions. I will describe in geometrical terms how a complete set of MUBs would sit in the set of density matrices and present a distance between bases–a measure of unbiasedness. Then I will explain the relation between MUBs and Hadamard matrices, and report on a search for MUB-sets in dimension N=6. In this case no sets of more than three MUBs are found, but there are several inequivalent triplets.

I\'ll introduce a particular class of fundamental string configurations in the form of closed loops stabilized by internal dynamics. I\\\'ll describe their classical treatment and embedding in models of string cosmology. I\\\'ll present the quantum version and the semiclassical limit that provides a microscopic description of dipole black rings. I\\\'ll show the parametric matching between the degeneracy of microstates and the entropy of the supergravity solution.

Loop Quantum Gravity and Deformation Quantization Abstract: We propose a unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo--Riemannian manifolds enabled with 1) a nonholonomic 2+2 distribution defining a nonlinear connection (N--connection) structure and 2) an ADM 3+1 decomposition. The Ashtekar-Barbero variables are generalized and adapted to the N-connection structure which allows us to write the general relativity theory equivalently in terms of Lagrange-Finsler variables and related canonical almost symplectic forms and connections. The Fedosov results are re-defined for gravitational gauge like connections and there are analyzed the conditions when the star product for deformation quantization is computed in terms of geometric objects in loop quantum gravity. We speculate on equivalence of quantum gravity theories with 3+1 and 2+2 splitting and quantum analogs of the Einstein equations.

The \\\"frequency comb\\\" defined by the eigenmodes of an optical resonator is a naturally large set of exquisitely well defined quantum systems, such as in the broadband mode-locked lasers which have redefined time/frequency metrology and ultra precise measurements in recent years. High coherence can therefore be expected in the quantum version of the frequency comb, in which nonlinear interactions couple different cavity modes, as can be modeled by different forms of graph states. We show that is possible to thereby generate states of interest to quantum metrology and computing, such as multipartite entangled cluster and Greenberger-Horne-Zeilinger states.