Dirac Operator on a disk with global boundary conditions

We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the connection between our result and the index theorem.Comment: RevTeX, 11 pages. References adde

A calculation with a bi-orthogonal wavelet transformation

We explore the use of bi-orthogonal basis for continuous wavelet transformations, thus relaxing the so-called admissibility condition on the analyzing wavelet. As an application, we determine the eigenvalues and corresponding radial eigenfunctions of the Hamiltonian of relativistic Hydrogen-like atoms.Comment: 18 pages, see instead physics/970300

Determinants of Dirac operators with local boundary conditions

We study functional determinants for Dirac operators on manifolds with boundary. We give, for local boundary conditions, an explicit formula relating these determinants to the corresponding Green functions. We finally apply this result to the case of a bidimensional disk under bag-like conditions.Comment: standard LaTeX, 24 pages. To appear in Jour. Math. Phy

Confined two-dimensional fermions at finite density

We introduce the chemical potential in a system of two-dimensional massless fermions, confined to a finite region, by imposing twisted boundary conditions in the Euclidean time direction. We explore in this simple model the application of functional techniques which could be used in more complicated situations.Comment: 15 pages, LaTe

Massless fermions in a bag at finite density and temperature

We introduce the chemical potential in a system of massless fermions in a bag by impossing boundary conditions in the Euclidean time direction. We express the fermionic mean number in terms of a functional trace involving the Green's function of the boundary value problem, which we study analytically. Numerical evaluations are made, and an application to a simple hadron model is discussed.Comment: 14 pages, 3 figures, RevTe

Imidazole and imidazolium antibacterial drugs derived from amino acids

The antibacterial activity of imidazole and imidazolium salts is highly dependent upon their lipophilicity, which can be tuned through the introduction of different hydrophobic substituents on the nitrogen atoms of the imidazole or imidazolium ring of the molecule. Taking this into consideration, we have synthesized and characterized a series of imidazole and imidazolium salts derived from L-valine and L-phenylalanine containing different hydrophobic groups and tested their antibacterial activity against two model bacterial strains, Gram-negative E. coli and Gram-positive B. subtilis. Importantly, the results demonstrate that the minimum bactericidal concentration (MBC) of these derivatives can be tuned to fall close to the cytotoxicity values in eukaryotic cell lines. The MBC value of one of these compounds toward B. subtilis was found to be lower than the IC50 cytotoxicity value for the control cell line, HEK-293. Furthermore, the aggregation behavior of these compounds has been studied in pure water, in cell culture media, and in mixtures thereof, in order to determine if the compounds formed self-assembled aggregates at their bioactive concentrations with the aim of determining whether the monomeric species were in fact responsible for the observed antibacterial activity. Overall, these results indicate that imidazole and imidazolium compounds derived from L-valine and L-phenylalanine—with different alkyl lengths in the amide substitution—can serve as potent antibacterial agents with low cytotoxicity to human cell lines

On Matrix Superpotential and Three-Component Normal Modes

We consider the supersymmetric quantum mechanics (SUSY QM) with three- component normal modes for the Bogomol'nyi-Prasad-Sommerfield (BPS) states. An explicit form of the SUSY QM matrix superpotential is presented and the corresponding three-component bosonic zero-mode eigenfunction is investigated.Comment: 17 pages, no figure. Paper accepted for publication in Journal of Physics A: Mathematical and Theoretica

Finite density and temperature in hybrid bag models

We introduce the chemical potential in a system of two-flavored massless fermions in a chiral bag by imposing boundary conditions in the Euclidean time direction. We express the fermionic mean number in terms of a functional trace involving the Green function of the boundary value problem, which is studied analytically. Numerical evaluations for the fermionic number are presented.Comment: 19 pages, 4 figure

Remarks on Screening in a Gauge-Invariant Formalism

In this paper we display a direct and physically attractive derivation of the screening contribution to the interaction potential in the Chiral Schwinger model and generalized Maxwell-Chern-Simons gauge theory. It is shown that these results emerge naturally when a correct separation between gauge-invariant and gauge degrees of freedom is made. Explicit expressions for gauge-invariant fields are found.Comment: 13 pages, 1 figure, to appear in PR

Pole structure of the Hamiltonian ζ\zeta-function for a singular potential

We study the pole structure of the $\zeta$-function associated to the Hamiltonian $H$ of a quantum mechanical particle living in the half-line $\mathbf{R}^+$, subject to the singular potential $g x^{-2}+x^2$. We show that $H$ admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter $g$. The $\zeta$-functions of these operators present poles which depend on $g$ and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered.Comment: 12 pages, 1 figure, RevTeX. References added. Version to appear in Jour. Phys. A: Math. Ge