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In relativistic quantum field theory particles of half-integer spin must obey Fermi-Dirac statistics. Their quantum operators must anticommute at spacelike separation in contrast to commuting physical observables. We show that Fermi-Dirac…
The space of abelian functions of a principally polarized abelian variety J is studied as a module over the ring D of global holomorphic differential operators on J. We construct a D-free resolution in case the theta divisor is…
In symplectic mechanics, the magnetic term describing the interaction between a charged particle and an external magnetic field has to be introduced by hand. On the contrary, in generalised complex geometry, such magnetic terms in the…
We consider the theory of open bosonic string in massive background fields. The general structure of renormalization is investigated. A general covariant action for a string in background fields of the first massive level is suggested and…
The symmetric spaces that appear as moduli spaces in string theory and supergravity can be decomposed with explicit metrics using parabolic subgroups. The resulting isometry between the original moduli space and this decomposition can be…
We present a construction of fermionic operators in 3+1 dimensions in terms of bosonic fields in the framework of $QED_4$. The basic bosonic variables are the electric fields $E_i$ and their conjugate momenta $A_i$. Our construction…
We study a bosonic open string coupled to a tachyonic background field $T[X]$ and find that the tachyon field can effectively be replaced by a configuration of D-branes placed at either the zeros or the critical points of $T[X]$, depending…
A general method of constructing the Dirac operator for a randomly triangulated manifold is proposed. The fermion field and the spin connection live, respectively, on the nodes and on the links of the corresponding dual graph. The…
We examine the effects of gravitational fields produced by topological defects on a Dirac field and a Dirac oscillator in a spinning cosmic string spacetime. We obtain the eigenfunctions and the energy levels of the relativistic field in…
We develop a method to determine the eigenvalues and eigenfunctions of two-boson Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential…
We determine what should correspond to the Dirac operator on certain quantized hermitian symmetric spaces and what its properties are. A new insight into the quantized wave operator is obtained.
We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli…
The scalar functional determinants on sectors of the two-dimensional disc and spherical cap are determined for arbitrary angles (rational factors of $\pi$). The wholesphere and hemisphere expressions are also given, in low dimensions, for…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
A bosonic Laplacian is a conformally invariant second order differential operator acting on smooth functions defined on domains in Euclidean space and taking values in higher order irreducible representations of the special orthogonal…
We exactly solve the (2+1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two 2-dimensional non-relativistic…
Dichroic signals derived from the Borrmann effect and a twisted photon beam with topological charge l = 1 are formulated with an effective wavevector. The unification applies for non-magnetic and magnetic materials. Electronic degrees of…
This is the first in a series of papers in which I investigate the orbifolds of permutation-type as candidates for {\it new physical string systems} at multiples of critical closed-string central charges. Examples include the bosonic…
We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…
The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…