[en] We reformulate in a systematic way the conversional approach in its most general and compact form. We present a new definition of generalized Dirac bracket directly in terms of the super-observables commuting with the basic BFV-BRST charge.

[en] We propose a new vector potential for the Abelian magnetic monopole. The potential is non-singular in the entire region around the monopole. We criticize Wu and Yang's derivation of the Dirac quantization condition, and argue how the condition can be derived for any choice of potential. Unlike the Wu-Yang case where two patches are needed to define the full potential, our potential needs only a single patch

No abstract available

[en] By a series of simple examples, we illustrate how the lack of mathematical concern can readily lead to surprising mathematical contradictions in wave mechanics. The basic mathematical notions allowing for a precise formulation of the theory are then summarized and it is shown how they lead to an elucidation and deeper understanding of the aforementioned problems. After stressing the equivalence between wave mechanics and the other formulations of quantum mechanics, i.e. matrix mechanics and Dirac's abstract Hilbert space formulation, we devote the second part of our paper to the latter approach: we discuss the problems and shortcomings of this formalism as well as those of the bra and ket notation introduced by Dirac in this context. In conclusion, we indicate how all of these problems can be solved or at least avoided. (author)

[en] The study of hidden symmetries within Dirac's formalism does not possess a systematic procedure due to the lack of first-class constraints to act as symmetry generators. On the other hand, in the Fadeev-Jackiw approach, gauge and reparameterization symmetries are generated by the null eigenvectors of the sympletic matrix and not by constraints, suggesting the possibility of dealing systematically with hidden symmetries throughout this formalism. It is shown in this paper that indeed hidden symmetries of noninvariant or gauge fixed systems are equally well described by null eigenvectors of the sympletic matrix, just as the explicit invariances. The Faddeev-Jackiw approach therefore provide a systematic algorithm for treating all sorts of symmetries in an unified way. This technique is illustrated here by the SL(2,R) affine Lie algebra of the 2D induced gravity proposed by Polyakov, which is a hidden symmetry in the canonical approach of constrained systems via Dirac's method, after conformal and reparameterization invariances have been fixed. 34 refs

[en] The string action enjoys Sierra's bosonic local symmetry on which Siegel's k-symmetry closes. This bosonic symmetry is analyzed in Dirac's Hamiltonian formalism and its generators are identified. (author)

[en] We refute the remarks made by Latimer, Comment on 'Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty' [Phys. Rev. A 75, 066101 (2007)]

[en] The effect of disorder on the Landau levels of massless Dirac fermions is examined for the cases with and without the fermion doubling. To tune the doubling a tight-binding model having a complex transfer integral is adopted to shift the energies of two Dirac cones, which is theoretically proposed earlier and realizable in cold atoms in an optical lattice. In the absence of the fermion doubling, the n = 0 Landau level is shown to exhibit an anomalous sharpness even if the disorder is uncorrelated in space (i.e., large K-K' scattering). This anomaly occurs when the disorder respects the chiral symmetry of the Dirac cone

[en] A relativistic two-particle radial equation describing a particle-antiparticle system with a Dirac oscillator interaction is written and solved by means of the 1/N expansion. The emerging picture of Dirac-oscillator mesons seems to be in qualitative agreement with meson phenomenology. The spectrum of excitation energies, the strong interaction radii, and the decay widths of states in our model are calculated and compared with the corresponding experimental magnitudes for mesons with a pure quark composition and total momentum J=L. (author). 15 refs, 3 figs

[en] We have addressed the dynamical conductivity of AA-stacked bilayer graphene as a function of photon frequency in the presence of a finite bias voltage at finite temperature. Using linear response theory and Green's function approach, the frequency dependence of optical conductivity has been obtained in the context of tight binding model Hamiltonian. Our results show a finite Drude absorption at low frequency for the case of charge neutrality. However, Drude weight gets remarkable amount at unbiased case. We have studied the behavior of optical spectra as a function of chemical potential for different values of bias voltages. Dynamical conductivity is found to be monotonically decreasing with chemical potential due to increased scattering among electrons at higher chemical potential. Furthermore the dependence of optical conductivity on the voltage bias and temperature has been investigated in details. (author)