10 problems

The dynamical spherical MIT bag has a moving boundary, and the fermion field satisfies the MIT bag boundary conditions at that boundary. In the massive case, the field cannot be wr…

The Dirac-Hestenes equation (DHE) is considered for potentials with prescribed symmetries, using either the Cartesian gauge or a gauge exhibiting the symmetry of the potential. Con…

Dirac's conjecture. The vacuum should be formed of a “sea” of quantum mechanical particles of negative energy.

Musès's conjecture. A simpler version of Dirac's equation using only the 16-dimensional $M$-algebra, namely the complex octonions, is possible.

Consider the periodically forced Dirac equation with mass $m=1$, and let $M^n$ denote its $n$-period propagator. For $\beta>0$, write…

Sharp spinor Sobolev constant conjecture. The sharp constant in the spinor Sobolev inequality is attained for these functions. Finding the optimal constants in the vector-field and…

Let $q$ be the strength of the Coulomb potential in the one-particle Dirac Hamiltonian … Here $c$ is the speed of light, $\hbar$ is the reduced Planck constant, $m$ is the particle…

Nonexistence conjecture. There are no nodal solutions with more than one sign change, namely

On a compact Riemann surface, a phase transformation relating the zero-energy Dirac equation in a magnetic field to meromorphic functions is considered, and the existence of noncon…

Let the metric be flat, let $\xi$ be a spinor field, and consider a plane-wave perturbation … where $\zeta$ is slowly varying, meaning that its second derivatives can be neglected…