Supercharge Operator of Hidden Symmetry in the Dirac Equation

As is known, the so-called Dirac $K$-operator commutes with the Dirac Hamiltonian for arbitrary central potential $V(r)$. Therefore the spectrum is degenerate with respect to two signs of its eigenvalues. This degeneracy may be described by some operator, which anticommutes with $K$. If this operator commutes with the Dirac Hamiltonian at the same time, then it establishes new symmetry, which is Witten's supersymmetry. We construct the general anticommuting with $K$ operator, which under the requirement of this symmetry unambiguously select the Coulomb potential. In this particular case our operator coincides with that, introduced by Johnson and Lippmann many years ago.Comment: 3 page

Nitrogen Fixation Mutants of the Actinobacterium Frankia Casuarinae CcI3

Frankia is a representative genus of nitrogen-fixing (N2-fixing) actinobacteria; however, the molecular mechanisms underlying various phenomena such as the differentiation of a N2 fixation-specific structure (vesicle) and the regulation of N2 fixation (nif) genes, have yet to be elucidated in detail. In the present study, we screened hyphal fragments of Frankia casuarinae that were mutagenized by 1-methyl-3-nitro-1-nitrosoguanidine or gamma rays, and isolated 49 candidate N2 fixation mutants. Twelve of these mutants were selected for further study, and their abilities to grow in NH3-deficient (N-) liquid media and their rates of acetylene reduction activities were evaluated. Eleven mutant strains were confirmed to lack the ability to fix N2. Five mutant strains formed significantly reduced numbers of vesicles, while some failed to form large mature vesicles. These vesicle mutants also exhibited an aberrant hyphal morphology, suggesting a relationship between vesicle differentiation and hyphal branching. Ten mutants showed significant reductions in the expression of nifE, nifH, and nifV genes under N- conditions. The genome sequencing of eight mutants identified 20 to 400 mutations. Although mutant strains N3H4 and N6F4 shared a large number of mutations (108), most were unique to each strain. Mutant strain N7C9 had 3 mutations in the nifD and nifH genes that may result in the inability to fix N2. The other mutant strains did not have any mutations in any known N2 fixation-related genes, indicating that they are novel N2 fixation mutants