Diffeomorphisms as Symplectomorphisms in History Phase Space: Bosonic String Model

The structure of the history phase space $\cal G$ of a covariant field system and its history group (in the sense of Isham and Linden) is analyzed on an example of a bosonic string. The history space $\cal G$ includes the time map $\sf T$ from the spacetime manifold (the two-sheet) $\cal Y$ to a one-dimensional time manifold $\cal T$ as one of its configuration variables. A canonical history action is posited on $\cal G$ such that its restriction to the configuration history space yields the familiar Polyakov action. The standard Dirac-ADM action is shown to be identical with the canonical history action, the only difference being that the underlying action is expressed in two different coordinate charts on $\cal G$. The canonical history action encompasses all individual Dirac-ADM actions corresponding to different choices $\sf T$ of foliating $\cal Y$. The history Poisson brackets of spacetime fields on $\cal G$ induce the ordinary Poisson brackets of spatial fields in the instantaneous phase space ${\cal G}_{0}$ of the Dirac-ADM formalism. The canonical history action is manifestly invariant both under spacetime diffeomorphisms Diff$\cal Y$ and temporal diffeomorphisms Diff$\cal T$. Both of these diffeomorphisms are explicitly represented by symplectomorphisms on the history phase space $\cal G$. The resulting classical history phase space formalism is offered as a starting point for projection operator quantization and consistent histories interpretation of the bosonic string model.Comment: 45 pages, no figure

Star products and perturbative quantum field theory

We discuss the application of the deformation quantization approach to perturbative quantum field theory. We show that the various forms of Wick's theorem are a direct consequence of the structure of the star products. We derive the scattering function for a free scalar field in interaction with a spacetime-dependent source. We show that the translation to operator formalism reproduces the known relations which lead to the derivation of the Feynman rules.Comment: 12 page

On the B\"acklund Transformation for the Moyal Korteweg-de Vries Hierarchy

We study the B\"acklund symmetry for the Moyal Korteweg-de Vries (KdV) hierarchy based on the Kuperschmidt-Wilson Theorem associated with second Gelfand-Dickey structure with respect to the Moyal bracket, which generalizes the result of Adler for the ordinary KdV.Comment: 9 pages, Revte

Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of semiquantum approximations to classical mechanics are indicated.Comment: 10 pages, Latex2e file, references added, minor clarifications mad

Perturbation theory of the space-time non-commutative real scalar field theories

The perturbative framework of the space-time non-commutative real scalar field theory is formulated, based on the unitary S-matrix. Unitarity of the S-matrix is explicitly checked order by order using the Heisenberg picture of Lagrangian formalism of the second quantized operators, with the emphasis of the so-called minimal realization of the time-ordering step function and of the importance of the $\star$-time ordering. The Feynman rule is established and is presented using $\phi^4$ scalar field theory. It is shown that the divergence structure of space-time non-commutative theory is the same as the one of space-space non-commutative theory, while there is no UV-IR mixing problem in this space-time non-commutative theory.Comment: Latex 26 pages, notations modified, add reference

Early structural brain development in infants exposed to HIV and antiretroviral therapy in utero in a South African birth cohort

INTRODUCTION: There is a growing population of children who are HIV-exposed and uninfected (HEU) with the successful expansion of antiretroviral therapy (ART) use in pregnancy. Children who are HEU are at risk of delayed neurodevelopment; however, there is limited research on early brain growth and maturation. We aimed to investigate the effects of in utero exposure to HIV/ART on brain structure of infants who are HEU compared to HIV-unexposed (HU). METHODS: Magnetic resonance imaging using a T2-weighted sequence was undertaken in a subgroup of infants aged 2–6 weeks enrolled in the Drakenstein Child Health Study birth cohort, South Africa, between 2012 and 2015. Mother–child pairs received antenatal and postnatal HIV testing and ART per local guidelines. We compared subcortical and total grey matter volumes between HEU and HU groups using multivariable linear regression adjusting for infant age, sex, intracranial volume and socio-economic variables. We further assessed associations between brain volumes with maternal CD4 cell count and ART exposure. RESULTS: One hundred forty-six infants (40 HEU; 106 HU) with high-resolution images were included in this analysis (mean age 3 weeks; 50.7% male). All infants who were HEU were exposed to ART (88% maternal triple ART). Infants who were HEU had smaller caudate volumes bilaterally (5.4% reduction, p 0.2). Total grey matter volume was also reduced in infants who were HEU (2.1% reduction, p < 0.05). Exploratory analyses showed that low maternal CD4 cell count (<350 cells/mm3) was associated with decreased infant grey matter volumes. There was no relationship between timing of ART exposure and grey matter volumes. CONCLUSIONS: Lower caudate and total grey matter volumes were found in infants who were HEU compared to HU in the first weeks of life, and maternal immunosuppression was associated with reduced volumes. These findings suggest that antenatal HIV exposure may impact early structural brain development and improved antenatal HIV management may have the potential to optimize neurodevelopmental outcomes of children who are HEU

BPS Configurations in Smectics

It is typical in smectic liquid crystals to describe elastic deformations with a linear theory when the elastic strain is small. We extend the recent, exact solution of Brener and Marchenko to more general one-dimensional deformations, including multiple edge dislocations by relying on the Bogomol'nyi, Prasad and Sommerfield (BPS) decomposition. We introduce an approximation for the deformation profile far from a spherical inclusion and find an enhanced attractive interaction at long distances due to the nonlinear elasticity.Comment: 4 pages, RevTeX, 2 figures, corrected typo

Synthetic methodology towards allylic trans-cyclooctene-ethers enables modification of carbohydrates: bioorthogonal manipulation of the lac repressor.

The inverse electron-demand Diels-Alder (IEDDA) pyridazine elimination is one of the key bioorthogonal bond-breaking reactions. In this reaction trans-cyclooctene (TCO) serves as a tetrazine responsive caging moiety for amines, carboxylic acids and alcohols. One issue to date has been the lack of synthetic methods towards TCO ethers from functionalized (aliphatic) alcohols, thereby restricting bioorthogonal utilization. Two novel reagents were developed to enable controlled formation of cis-cyclooctene (CCO) ethers, followed by optimized photochemical isomerization to obtain TCO ethers. The method was exemplified by the controlled bioorthogonal activation of the lac operon system in E. coli using a TCO-ether-modified carbohydrate inducer.Bio-organic Synthesi

A finite model of two-dimensional ideal hydrodynamics

A finite-dimensional su($N$) Lie algebra equation is discussed that in the infinite $N$ limit (giving the area preserving diffeomorphism group) tends to the two-dimensional, inviscid vorticity equation on the torus. The equation is numerically integrated, for various values of $N$, and the time evolution of an (interpolated) stream function is compared with that obtained from a simple mode truncation of the continuum equation. The time averaged vorticity moments and correlation functions are compared with canonical ensemble averages.Comment: (25 p., 7 figures, not included. MUTP/92/1