Non-unitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential

A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that, besides, allow the factorization of the problem. An extra phase is needed as a new variable in order to define the algebra. We take advantage of the operators to solve the Dirac equation using algebraic methods. To acomplish this, a similar path to the one used in the angular momentum case is employed; hence, the radial eigenfuntions calculated comprise non unitary representations of the algebra. One of the interesting properties of such non unitary representations is that they are not labeled by integer nor by half-integer numbers as happens in the usual angular momentum representation.Comment: 20 pages 1 eps figure in a single zipped file, submitted to J. Math. Phy

Lagrangian Description of the Variational Equations

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. Our main result establishes that both the Euler-Lagrange equations and the corresponding variational equations of the original system can be viewed as the Lagrangian vector field associated with the first prolongation of the original LagrangianAfter discussing certain features of the formulation, we introduce the so-called inherited constants of the motion and relate them to the Noether constants of the extended system

Effect of Expression of the Aphthovirus Protease 3C on Viral Infection and Gene Expression

AbstractCells transformed with specific regions of the foot-and-mouth disease virus (FMDV) genome have been constructed and analyzed with respect to viability and susceptibility to FMDV infection. Constitutive expression of an active protease 3C under the control of the tk promoter has been documented by the ability of transformed cells to catalyze the processing of a P1 capsid precursor. High-level, transient expression but not low-level, constitutive expression, of 3C caused a 10-fold reduction in the yield of FMDV and was detrimental to the expression of the cotransfected reporter luciferase gene. No such effect was observed in assays involving cells transfected with a deleted, inactive form of 3C. The negative effect of 3C was not observed when the same reporter gene was integrated and expressed in a constitutive fashion nor when its translation was directed by the internal ribosome entry site element of FMDV in transient expression assays. The results show that cells with a low level of expression of the aphthoviral 3C can be stably maintained and can provide a useful tool to study polyprotein processing

Immunogenicity and T cell recognition in swine of foot-and-mouth disease virus polymerase 3D

Immunization of domestic pigs with a vaccinia virus (VV) recombinant expressing foot-and-mouth disease virus (FMDV) 3D protein conferred partial protection against challenge with infectious virus. The severity reduction of the clinical symptoms developed by the challenged animals occurred in the absence of significant levels of anti-3D circulating antibodies. This observation suggested that the partial protection observed was mediated by the induction of a 3D-specific cellular immune response. To gain information on the T cell recognition of FMDV 3D protein, we conducted in vitro proliferative assays using lymphocytes from outbred pigs experimentally infected with FMDV and 90 overlapping peptides spanning the complete 3D sequence. The use of pools of two to three peptides allowed the identification of T cell epitopes that were efficiently recognized by lymphocytes from at least four of the five animals analyzed. This recognition was heterotypic because anti-peptide responses increased upon reinfection of animals with a FMDV isolate from a different serotype. The results obtained with individual peptides confirmed the antigenicity observed with peptide pools. Detection of cytokine mRNAs by RT-PCR in lymphocytes stimulated in vitro by individual 3D peptides revealed that IFN-γ mRNA was the most consistently induced, suggesting that the activated T cells belong to the Th 1 subset. These results indicate that 3D protein contains epitopes that can be efficiently recognized by porcine T lymphocytes from different infected animals, both upon primary and secondary (heterotypic) FMDV infection. These epitopes can extend the repertoire of viral T cell epitopes to be included in subunit and synthetic FMD vaccines. © 2004 Elsevier Inc. All rights reserved