Perturbative Inaccessibility of Conformal Fixed Points in Nonsupersymmetric Quiver Theories

The possibility that non-supersymmetric quiver theories may have a renormalization-group fixed point at which there is conformal invariance requires non-perturbative information.The possibility that non-supersymmetric quiver theories may have a renormalization-group fixed point at which there is conformal invariance requires non-perturbative information

Observation of a push force on the end face of a nm fiber taper exerted by outgoing light

There are two different proposals for the momentum of light in a transparent dielectric of refractive index n: Minkowski's version nE/c and Abrahm's version E/(nc), where E and c are the energy and vacuum speed of light, respectively. Despite many tests and debates over nearly a century, momentum of light in a transparent dielectric remains controversial. In this Letter, we report a direct observation of the inward push force on the end face of a free nm fiber taper exerted by the outgoing light. Our results clearly support Abraham momentum. Our experiment also indicates an inward surface pressure on a dielectric exerted by the incident light, different from the commonly recognized pressure due to the specular reflection. Such an inward surface pressure by the incident light may be useful for precise design of the laser-induced inertially-confined fusion.Comment: 9 pages, 3 figures;Accepted for publication as a Letter in Physical Review Letters(CODE: LP11093

The Red Queen visits Minkowski Space

When Alice went `Through the Looking Glass' [1], she found herself in a situation where she had to run as fast as she could in order to stay still. In accordance with the dictum that truth is stranger than fiction, we will see that it is possible to find a situation in special relativity where running towards one's target is actually counter-productive. Although the situation is easily analysed algebraically, the qualitative properties of the analysis are greatly illuminated by the use of space-time diagrams

Estimates of the optimal density and kissing number of sphere packings in high dimensions

The problem of finding the asymptotic behavior of the maximal density of sphere packings in high Euclidean dimensions is one of the most fascinating and challenging problems in discrete geometry. One century ago, Minkowski obtained a rigorous lower bound that is controlled asymptotically by $1/2^d$, where $d$ is the Euclidean space dimension. An indication of the difficulty of the problem can be garnered from the fact that exponential improvement of Minkowski's bound has proved to be elusive, even though existing upper bounds suggest that such improvement should be possible. Using a statistical-mechanical procedure to optimize the density associated with a "test" pair correlation function and a conjecture concerning the existence of disordered sphere packings [S. Torquato and F. H. Stillinger, Experimental Math. {\bf 15}, 307 (2006)], the putative exponential improvement was found with an asymptotic behavior controlled by $1/2^{(0.77865...)d}$. Using the same methods, we investigate whether this exponential improvement can be further improved by exploring other test pair correlation functions correponding to disordered packings. We demonstrate that there are simpler test functions that lead to the same asymptotic result. More importantly, we show that there is a wide class of test functions that lead to precisely the same exponential improvement and therefore the asymptotic form $1/2^{(0.77865...)d}$ is much more general than previously surmised.Comment: 23 pages, 4 figures, submitted to Phys. Rev.

Discreteness of the volume of space from Bohr-Sommerfeld quantization

A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space itself. We compute the Bohr-Sommerfeld volume spectrum of a tetrahedron and show that it reproduces the quantization of a grain of space found in loop gravity.Comment: 4 pages, 4 figures; v2, to appear in PR

A Potential Foundation for Emergent Space-Time

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an observer can consistently quantify events and their relationships to one another. The result is a potential foundation for emergent space-time.Comment: The paper was originally titled "The Physics of Events: A Potential Foundation for Emergent Space-Time". We changed the title (and abstract) to be more direct when the paper was accepted for publication at the Journal of Mathematical Physics. 24 pages, 15 figure

On the quest for unification - simplicity and antisimplicity

The road towards unification of elementary interactions is thought to start on the solid ground of a universal local gauge principle. I discuss the different types of bosonic gauge symmetries in gravitational and nongravitational (standard model) interactions and their extensions both fermionic, bosonic and with respect to space-time dimensions. The apparently paradoxical size and nature of the cosmological constant is sketched, which at first sight does not readily yield a clue as to the envelopping symmetry structure of a unified theory. Nevertheless a tentative outlook is given encouraging to proceed on this road.Comment: 29 pages, 4 figure

Perspectives: Quantum Mechanics on Phase Space

The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical particle model descriptions exhibiting either Galileian or Lorentzian symmetry. The structures of fundamental importance are the relevant (Lie) groups of symmetries and their homogeneous (and associated) spaces that, in the situations of interest, also possess Hamiltonian structures. Comments are made on the relation between the theory outlined and a recent paper by Carmeli, Cassinelli, Toigo, and Vacchini.Comment: "Quantum Structures 2004" - Meeting of the International Quantum Structures Association; Denver, Colorado; 17-22 July, 200

Quantum Vacuum Contribution to the Momentum of the Dielectric Media

Momentum transfer between matter and electromagnetic field is analyzed. The related equations of motion and conservation laws are derived using relativistic formalism. Their correspondence to various, at first sight self-contradicting, experimental data (the so called Abraham-Minkowski controversy) is demonstrated. A new, Casimir like, quantum phenomenon is predicted: contribution of vacuum fluctuations to the motion of dielectric liquids in crossed electric and magnetic fields. Velocities about $50nm/s$ can be expected due to the contribution of high frequency vacuum modes

A Dense Packing of Regular Tetrahedra

We construct a dense packing of regular tetrahedra, with packing density $D > >.7786157$.Comment: full color versio