Quantum Dirac fermions in half space and their interaction with electromagnetic field

Understand

We study the polarization tensor of a Dirac field in $(3+1)$ dimensions confined to a half space -- a problem motivated by applications to the condensed matter physics, and to Topological Insulators in particular.

• Although the Pauli-Villars regularization scheme has a number of advantages, like explicit gauge invariance and decoupling of heavy modes, it is not applicable on manifolds with boundaries.
• Here, we modify this scheme by giving an axial mass to the regulators and to the physical field.
• We compute the renormalized polarization tensor in coordinate representation.