BF Actions for the Husain-Kuchar Model

We show that the Husain-Kuchar model can be described in the framework of BF theories. This is a first step towards its quantization by standard perturbative QFT techniques or the spin-foam formalism introduced in the space-time description of General Relativity and other diff-invariant theories. The actions that we will consider are similar to the ones describing the BF-Yang-Mills model and some mass generating mechanisms for gauge fields. We will also discuss the role of diffeomorphisms in the new formulations that we propose.Comment: 21 pages (in DIN A4 format), minor typos corrected; to appear in Phys. Rev.

The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian

The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points $V_1$ and $V_2$ in the big cell \Gr of the Sato Grassmannian $Gr$. This is a consequence of a well-defined continuum limit in which the string equation has the simple form \lb \cp ,\cq_- \rb =\hbox{\rm 1}, with \cp and \cq_- $2\times 2$ matrices of differential operators. These conditions on $V_1$ and $V_2$ yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints \L_n\,(n\geq 0), where \L_n annihilate the two modified-KdV \t-functions whose product gives the partition function of the Unitary Matrix Model.Comment: 21 page

On Integrable c<1 Open--Closed String Theory

The integrable structure of open--closed string theories in the $(p,q)$ conformal minimal model backgrounds is presented. The relation between the $\tau$--function of the closed string theory and that of the open--closed string theory is uncovered. The resulting description of the open--closed string theory is shown to fit very naturally into the framework of the $sl(q,{\rm C})$ KdV hierarchies. In particular, the twisted bosons which underlie and organise the structure of the closed string theory play a similar role here and may be employed to derive loop equations and correlation function recursion relations for the open--closed strings in a simple way.Comment: (Slight corrections to title, text, terminology and references. Note added. No change in physics.) , 30pp, IASSNS--HEP--93/

A Matrix Integral Solution to [P,Q]=P and Matrix Laplace Transforms

In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P,Q]=P, where P flows according to the KP hierarchy \partial P/\partial t_n = [(P^{n/p})_+,P], with p := \ord P\ge 2; (ii) find a matrix integral representation for the associated \t au-function. First we construct an infinite dimensional space {\cal W}=\Span_\BC \{\psi_0(z),\psi_1(z),... \} of functions of z\in\BC invariant under the action of two operators, multiplication by z^p and A_c:= z \partial/\partial z - z + c. This requirement is satisfied, for arbitrary p, if \psi_0 is a certain function generalizing the classical H\"ankel function (for p=2); our representation of the generalized H\"ankel function as a double Laplace transform of a simple function, which was unknown even for the p=2 case, enables us to represent the \tau-function associated with the KP time evolution of the space \cal W as a ``double matrix Laplace transform'' in two different ways. One representation involves an integration over the space of matrices whose spectrum belongs to a wedge-shaped contour \gamma := \gamma^+ + \gamma^- \subset\BC defined by \gamma^\pm=\BR_+\E^{\pm\pi\I/p}. The new integrals above relate to the matrix Laplace transforms, in contrast with the matrix Fourier transforms, which generalize the Kontsevich integrals and solve the operator equation [P,Q]=1.Comment: 27 pages, LaTeX, 1 figure in PostScrip

Canonical Structure of Classical Field Theory in the Polymomentum Phase Space

Canonical structure of the space-time symmetric analogue of the Hamiltonian formalism in field theory based on the De Donder-Weyl (DW) theory is studied. In $n$ space-time dimensions the set of $n$ polymomenta is associated to the space-time derivatives of field variables. The polysymplectic $(n+1)$-form generalizes the simplectic form and gives rise to a map between horizontal forms playing the role of dynamical variables and vertical multivectors generalizing Hamiltonian vector fields. Graded Poisson bracket is defined on forms and leads to the structure of a Z-graded Lie algebra on the subspace of the so-called Hamiltonian forms for which the map above exists. A generalized Poisson structure arises in the form of what we call a ``higher-order'' and a right Gerstenhaber algebra. Field euations and the equations of motion of forms are formulated in terms of the graded Poisson bracket with the DW Hamiltonian $n$-form H\vol (\vol is the space-time volume form and $H$ is the DW Hamiltonian function). A few applications to scalar fields, electrodynamics and the Nambu-Goto string, and a relation to the standard Hamiltonian formalism in field theory are briefly discussed. This is a detailed and improved account of our earlier concise communications (hep-th/9312162, hep-th/9410238, and hep-th/9511039).Comment: 45 pages, LaTeX2e, to appear in Reports on Mathematical Physics v. 41 No. 1 (1998

Background-Independence

Intuitively speaking, a classical field theory is background-independent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails.Comment: Forthcoming in General Relativity and Gravitatio

Modern venomics – Current insights, novel methods and future perspectives in biological and applied animal venom research

Venoms have evolved &gt;100 times in all major animal groups, and their components, known as toxins, have been fine-tuned over millions of years into highly effective biochemical weapons. There are many outstanding questions on the evolution of toxin arsenals, such as how venom genes originate, how venom contributes to the fitness of venomous species, and which modifications at the genomic, transcriptomic, and protein level drive their evolution. These questions have received particularly little attention outside of snakes, cone snails, spiders, and scorpions. Venom compounds have further become a source of inspiration for translational research using their diverse bioactivities for various applications. We highlight here recent advances and new strategies in modern venomics and discuss how recent technological innovations and multi-omic methods dramatically improve research on venomous animals. The study of genomes and their modifications through CRISPR and knockdown technologies will increase our understanding of how toxins evolve and which functions they have in the different ontogenetic stages during the development of venomous animals. Mass spectrometry imaging combined with spatial transcriptomics, in situ hybridization techniques, and modern computer tomography gives us further insights into the spatial distribution of toxins in the venom system and the function of the venom apparatus. All these evolutionary and biological insights contribute to more efficiently identify venom compounds, which can then be synthesized or produced in adapted expression systems to test their bioactivity. Finally, we critically discuss recent agrochemical, pharmaceutical, therapeutic, and diagnostic (so-called translational) aspects of venoms from which humans benefit

Danube and Sava river sediment monitoring in Belgrade and its surroundings

Belgrade is the largest city in Serbia located at the confluence of river Sava to the Danube river. The quality of water and sediments of rivers which run through Belgrade is of a significant importance, since water from these rivers is a source of Belgrade drinking water supply system and probable anthropogenic contamination is related to industrialization and inputs of sewage water. In order to follow the sediment quality of river Sava (km 62-1) and river Danube (km 1193-1124) in Belgrade and its surroundings, the content of As, Cd, Cr, Cu, Zn, Ni, Pb and Hg were measured in the period 2001-2005. The content of 16 polycyclic aromatic hydrocarbons (PAHs) was measured in 2005. The results have shown that, due to the metal content, examined Danube sediment quality varies from class 1 to class 3, predominantly nickel being the class determining parameter. Elevated copper, zinc and mercury concentrations were measured at some profiles, as well. Typically due to the nickel content, Sava sediment quality belongs to class 3 in the period 2001-2004. Elevated concentrations of cadmium, zinc and mercury were observed in 2001, as well. Moreover, in 2005, sediments from three profiles were extremely polluted with nickel, leading the Sava sediment to class 4, when highest urgency measures are needed. Total PAH concentration in the sediments from Danube (213.1-575.4 mu g kg(-1)) was lower than total PAH concentration from Sava sediments (416.2-595.3 mu g kg(-1)). Nevertheless, according to the Dutch regulatory system, it has been concluded that river sediments in Belgrade and its surroundings were not polluted with PAHs in 2005