Related papers: Quantum Dirac field without vacuum energy divergen…
We address the problems of an energy spectrum and backscattering of massive Dirac fermions confined in a cylindrical quantum wire. The Dirac fermions are described by the 3D Dirac equation supplemented by time-reversal-invariant boundary…
The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…
We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic…
The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space…
I investigate three dimensional abelian and non-abelian gauge theories interacting with Dirac fermions. Using a variational method I evaluate the vacuum energy density in the one-loop approximation. It turns out that the states with a…
We consider full phase-space noncommutativity in the Dirac equation, and find that in order to preserve gauge invariance, configuration space noncommutativity must be dropped. The resulting space structure gives rise to a constant magnetic…
On a static spacetime, the solutions of the Dirac equation are generated by a time-independent Hamiltonian. We study this Hamiltonian and characterize the split into positive and negative energy. We use it to find explicit expressions for…
We consider a U(1) gauge theory, minimally coupled to a massless Dirac field, where a higher-derivative term is added to the pure gauge sector, as in the Lee-Wick models. We find that this term can trigger chiral symmetry breaking at low…
Three out of four complex components of the Dirac spinor can be algebraically eliminated from the Dirac equation (if some linear combination of electromagnetic fields does not vanish), yielding a partial differential equation of the fourth…
The field theory quantized on the {\it light-front} is compared with the conventional equal-time quantized theory. The arguments based on the {\it microcausality} principle imply that the light-front field theory may become nonlocal with…
The energy density is computed for a U(2) Chern-Simons theory coupled to a non-relativistic fermion field (a theory of ``non-Abelian anyons'') under the assumptions of uniform charge and matter density. When the matter field is a spinless…
The free Dirac equation is solved in a Bianchi Type I space-time, which represents a homogeneous but anisotropic universe, to show the creation of fermionic particles. It is found that unlike in the isotropic case, massless fermion…
We consider a massive fermionic quantum field localized on a plane in external constant and homogeneous electric and magnetic fields. The magnetic field is perpendicular to the plane and the electric field is parallel. The complete set of…
The assumption that the vacuum is the minimum energy state, invariant under unitary transformations, is fundamental to quantum field theory. However, the assertion that the conservation of charge implies that the equal time commutator of…
The dynamics of a light fermion bound to a heavy one is expected to be described by the Dirac equation with an external potential. The potential breaks translation invariance, whereas the bound state momentum is well defined. Boosting the…
We investigate the vacuum polarization and the Casimir energy of a Dirac field coupled to a scalar potential in one spatial dimension. Both of these effects have a common cause which is the distortion of the spectrum due to the coupling…
We evaluate the dispersion relation for massless fermions, described by the Dirac equation, and for zero-spin bosons, described by the Klein-Gordon equation, moving in two dimensions and in the presence of a one-dimensional periodic…
The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it…
The continuous quantum phase transition between noninteracting, time-reversal symmetric topological and trivial insulators in three dimensions is described by the massless Dirac fermion. We address the stability of this quantum critical…
It is well known that there can be negative energy densities in quantum field theory. Most of the work done in this area has involved free non-interacting systems. In this paper we show how a quantum state with negative energy density can…