We develop relativistic wave equations in the framework of the new non-hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT -symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no cou...

The variational method is a powerful approach to solve many-body quantum problems nonperturbatively. However, in the context of relativistic field theory, it needs meet three seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack UV sensitivity. In practice, methods break one three, which translates into need have an IR or cutoff. this letter, I introduce ...

A relativistic density-functional theory based on a Fock-space effective quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit two-particle interaction is developed. This QED properly includes effects of vacuum polarization through creation electron-positron pairs but does not include explicitly photon degrees freedom. It thus more tractable alternative to full for atomic...

This essay considers the question of the ontology of relativistic quantum field theory (RQFT). It aims to discuss possible implications of the peculiarities of quantum entanglement and quantum non-locality within the algebraic approach to RQFT. Fundamental results such as the Reeh-Schlieder theorem do not only show that quantum entanglement is a truly central feature of RQFT, but also that quan...

The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic quantum mechanics algebra is also unstable. Its stabilization requires the non-commutativity of the space-time coordinates and the existence of a fundamental len...

We study the nonrelativistic limit of the theory of a quantum Chern–Simons field minimally coupled to Dirac fermions. To get the nonrelativistic effective Lagrangian one has to incorporate vacuum polarization and anomalous magnetic moment effects. Besides that, an unsuspected quartic fermionic interaction may also be induced. As a by product, the method we use to calculate loop diagrams, separa...