Factorization of Spanning Trees on Feynman Graphs

In order to use the Gaussian representation for propagators in Feynman amplitudes, a representation which is useful to relate string theory and field theory, one has to prove first that each $\alpha$- parameter (where $\alpha$ is the parameter associated to each propagator in the $\alpha$-representation of the Feynman amplitudes) can be replaced by a constant instead of being integrated over and second, prove that this constant can be taken equal for all propagators of a given graph. The first proposition has been proven in one recent letter when the number of propagators is infinite. Here we prove the second one. In order to achieve this, we demonstrate that the sum over the weighted spanning trees of a Feynman graph $G$ can be factorized for disjoint parts of $G$. The same can also be done for cuts on $G$, resulting in a rigorous derivation of the Gaussian representation for super-renormalizable scalar field theories. As a by-product spanning trees on Feynman graphs can be used to define a discretized functional space.Comment: 47 pages, Plain Tex, 3 PostScript figure

Fighting covid-19 outbreaks in prisons

Improving prison health services is critical for fighting epidemics such as covid-19. Prisoners are at much higher risk of infectious diseases than communities outside. Eruption of covid-19 in prisons emphasises the need to improve prison healthcare. Health education for inmates and prison staff must be intensified, and better treatment and prevention measures require increased funding. More non-custodial sentences would decongest prisons, reducing the potential for the outbreaks. Links between prison and national health services should be strengthened

Regge behaviour and Regge trajectory for ladder graphs in scalar Φ3\Phi^3 field theory

Using the gaussian representation for propagators (which can be proved to be exact in the infinite number of loops limit) we are able to derive the Regge behaviour for ladder graphs of $\phi^3$ field theory in a completely new way. An analytic expression for the Regge trajectory $\alpha (t/m^2)$ is found in terms of the mean-values of the Feynman $\alpha$-parameters. $\alpha (t/m^2)$ is calculated in the range $- 3.6 < t/m^2 < 0.8$. The intercept $\alpha (0)$ agrees with that obtained from earlier calculations using the Bethe-Salpeter approach for \alpha (0) \gsim 0.3.Comment: 10 PlainTex pages, 2 PostScript Figures include

Dispersion Laws for In-medium Fermions and Gluons in the CFL Phase of QCD

We evaluate several quantities appearing in the effective lagrangian for the color-flavor locked phase of high density QCD using a formalism which exploits the approximate decoupling of fermions with energy negative with respect to the Fermi energy. The effective theory is essentially two-dimensional and exhibits a Fermi velocity superselection rule, similar to the one found in the Heavy Quark Effective Theory. Within the formalism we reproduce, using gradient expansion, the results for the effective parameters of the Nambu-Goldstone bosons. We also determine the dispersion laws for the gluons. By coupling the theory to fermions and integrating over the two-dimensional degrees of freedom we obtain the effective description of in-medium fermions.Comment: 17 pages, LaTex, 2 figures. Version published in Phys. Lett. B with an arithmetic misprint corrected in eq. (62) (and as a consequence in eqs. (63), (66) and (73)

tRNA splicing

Introns interrupt the continuity of many eukaryal genes, and therefore their removal by splicing is a crucial step in gene expression. Interestingly, even within Eukarya there are at least four splicing mechanisms. mRNA splicing in the nucleus takes place in two phosphotransfer reactions on a complex and dynamic machine, the spliceosome. This reaction is related in mechanism to the two self-splicing mechanisms for Group 1 and Group 2 introns. In fact the Group 2 introns are spliced by an identical mechanism to mRNA splicing, although there is no general requirement for either proteins or co-factors. Thus it seems likely that the Group 2 and nuclear mRNA splicing reactions have diverged from a common ancestor. tRNA genes are also interrupted by introns, but here the splicing mechanism is quite different because it is catalyzed by three enzymes, all proteins and with an intrinsic requirement for ATP hydrolysis. tRNA splicing occurs in all three major lines of descent, the Bacteria, the Archaea, and the Eukarya. In bacteria the introns are self-splicing (1-3). Until recently it was thought that the mechanisms of tRNA splicing in Eukarya and Archaea were unrelated as well. In the past year, however, it has been found that the first enzyme in the tRNA splicing pathway, the tRNA endonuclease, has been conserved in evolution since the divergence of the Eukarya and the Archaea. Surprising insights have been obtained by comparison of the structures and mechanisms of tRNA endonuclease from these two divergent lines

Radiation generated by accelerating and rotating charged black holes in (anti-)de Sitter space

Asymptotic behaviour of gravitational and electromagnetic fields of exact type D solutions from the large Plebanski-Demianski family of black hole spacetimes is analyzed. The amplitude and directional structure of radiation is evaluated in cases when the cosmological constant is non-vanishing, so that the conformal infinities have either de Sitter-like or anti-de Sitter-like character. In particular, explicit relations between the parameters that characterize the sources (that is their mass, electric and magnetic charges, NUT parameter, rotational parameter, and acceleration) and properties of the radiation generated by them are presented. The results further elucidate the physical interpretation of these solutions and may help to understand radiative characteristics of more general spacetimes than those that are asymptotically flat.Comment: 24 pages, 18 figures. To appear in Classical and Quantum Gravit