Holographic Geometry and Noise in Matrix Theory

Using Matrix Theory as a concrete example of a fundamental holographic theory, we show that the emergent macroscopic spacetime displays a new macroscopic quantum structure, holographic geometry, and a new observable phenomenon, holographic noise, with phenomenology similar to that previously derived on the basis of a quasi-monochromatic wave theory. Traces of matrix operators on a light sheet with a compact dimension of size $R$ are interpreted as transverse position operators for macroscopic bodies. An effective quantum wave equation for spacetime is derived from the Matrix Hamiltonian. Its solutions display eigenmodes that connect longitudinal separation and transverse position operators on macroscopic scales. Measurements of transverse relative positions of macroscopically separated bodies, such as signals in Michelson interferometers, are shown to display holographic nonlocality, indeterminacy and noise, whose properties can be predicted with no parameters except $R$. Similar results are derived using a detailed scattering calculation of the matrix wavefunction. Current experimental technology will allow a definitive and precise test or validation of this interpretation of holographic fundamental theories. In the latter case, they will yield a direct measurement of $R$ independent of the gravitational definition of the Planck length, and a direct measurement of the total number of degrees of freedom.Comment: 19 pages, 2 figures; v2: factors of Planck mass written explicitly, typos correcte

Character-theoretic Techniques for Near-central Enumerative Problems

The centre of the symmetric group algebra $\mathbb{C}[\mathfrak{S}_n]$ has been used successfully for studying important problems in enumerative combinatorics. These include maps in orientable surfaces and ramified covers of the sphere by curves of genus $g$, for example. However, the combinatorics of some equally important $\mathfrak{S}_n$-factorization problems forces $k$ elements in $\{1,...,n\}$ to be distinguished. Examples of such problems include the star factorization problem, for which $k=1,$ and the enumeration of 2-cell embeddings of dipoles with two distinguished edges \cite{VisentinWieler:2007} associated with Berenstein-Maldacena-Nastase operators in Yang-Mills theory \cite{ConstableFreedmanHeadrick:2002}, for which $k=2.$ Although distinguishing these elements obstructs the use of central methods, these problems may be encoded algebraically in the centralizer of $\mathbb{C}[\mathfrak{S}_n]$ with respect to the subgroup $\mathfrak{S}_{n-k}.$ We develop methods for studying these problems for $k=1,$ and demonstrate their efficacy on the star factorization problem. In a subsequent paper \cite{JacksonSloss:2011}, we consider a special case of the the above dipole problem by means of these techniques

1/10 PROCESS FOR MAKING CHANGES IN WG1 QUALITY

Version: 2.

Thrombin exosite for fibrinogen recognition is partially accessible in prothrombin.

The procoagulant alpha-thrombin is produced by the proteolytic cleavages of a minimum of two peptide bonds Arg274-Thr275 and Arg323-Ile324 in prothrombin. The Arg323-Ile324 cleavage is required for the expression of the active site of thrombin (Morita, T., Iwanaga, S. Suzuki, T. (1976) J. Biochem. (Tokyo) 79, 1089-1108; Hibbard, L. S., Nesheim, M. E., and Mann, K. G. (1982) Biochemistry 21, 2285-2292). It is not yet clear to what extent the proteolytic events are responsible for exposing protein recognition exosites on thrombin. We employed high resolution NMR spectroscopy to examine interactions of prothrombin and thrombin with synthetic hirudin peptides targeted toward the fibrinogen recognition exosite of thrombin. The hirudin tail synthetic analogues (acetyl-Asp55-Phe-Glu-Glu-Ile-Pro-Glu-Glu-Tyr-Leu-Gln65/G ly65-OH) exhibited similar NMR relaxation enhancements (line broadening patterns and transferred nuclear Overhauser effects) with human prothrombin as with human alpha-thrombin, indicating that both proteins bind the peptide in a similar manner. The protein-induced relaxation enhancements are specific to the interaction of the hirudin peptides with the fibrinogen recognition exosite of thrombin since no significant effects were observed with either human serum albumin or with human gamma-thrombin, which has an impaired recognition exosite. The binding affinities were determined from NMR relaxation time measurements, which gave approximate Kd values of 500 microM an

Noncovariant gauge fixing in the quantum Dirac field theory of atoms and molecules

Starting from the Weyl gauge formulation of quantum electrodynamics (QED), the formalism of quantum-mechanical gauge fixing is extended using techniques from nonrelativistic QED. This involves expressing the redundant gauge degrees of freedom through an arbitrary functional of the gauge-invariant transverse degrees of freedom. Particular choices of functional can be made to yield the Coulomb gauge and Poincar\'{e} gauge representations. The Hamiltonian we derive therefore serves as a good starting point for the description of atoms and molecules by means of a relativistic Dirac field. We discuss important implications for the ontology of noncovariant canonical QED due to the gauge freedom that remains present in our formulation.Comment: 8 pages, 0 figure

Evidence for variable selective pressures at MC1R

It is widely assumed that genes that influence variation in skin and hair pigmentation are under selection. To date,the melanocortin 1 receptor (MC1R) is the only gene identified that explains substantial phenotypic variance inhuman pigmentation. Here we investigate MC1R polymorphism in several populations, for evidence of selection.We conclude that MC1R is under strong functional constraint in Africa, where any diversion from eumelanin production (black pigmentation) appears to be evolutionarily deleterious. Although many of the MC1R amino acid variants observed in non-African populations do affect MC1R function and contribute to high levels of MC1R diversity in Europeans, we found no evidence, in either the magnitude or the patterns of diversity, for its enhancement by selection; rather, our analyses show that levels of MC1R polymorphism simply reflect neutral expectations underrelaxation of strong functional constraint outside Africa

Quantum Electrodynamics near a Huttner-Barnett dielectric

We build up a consistent theory of quantum electrodynamics in the presence of macroscopic polarizable media. We use the Huttner-Barnett model of a dispersive and absorbing dielectric medium and formulate the theory in terms of interacting quantum fields. We integrate out the damped polaritons by using diagrammatic techniques and find an exact expression for the displacement field (photon) propagator in the presence of a dispersive and absorbing dielectric half-space. This opens a new route to traceable perturbative calculations of the same kind as in free-space quantum electrodynamics. As a worked-through example we consider the interaction of a neutral atom with a dispersive and absorbing dielectric half-space. For that we use the multipolar coupling $\boldsymbol{\mu}\cdot\mathbf{D}$ of the atomic dipole moment to the electromagnetic displacement field. We apply the newly developed formalism to calculate the one-loop correction to the atomic electron propagator and find the energy-level shift and changes in the spontaneous decay rates for a neutral atom close to an absorptive dielectric mirror.Comment: 25 pages, 4 figure

The role of angular momentum in the construction of electromagnetic multipolar fields

Multipolar solutions of Maxwell's equations are used in many practical applications and are essential for the understanding of light-matter interactions at the fundamental level. Unlike the set of plane wave solutions of electromagnetic fields, the multipolar solutions do not share a standard derivation or notation. As a result, expressions originating from different derivations can be difficult to compare. Some of the derivations of the multipolar solutions do not explicitly show their relation to the angular momentum operators, thus hiding important properties of these solutions. In this article, the relation between two of the most common derivations of this set of solutions is explicitly shown and their relation to the angular momentum operators is exposed.Comment: 13 pages, 2 figure

Optical Thomas-Reiche-Kuhn sum rules

The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region