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

Abstract

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. We discuss then the induced Chern-Simons type action on the boundary and compare it to the effective action of a $(2+1)$ dimensional Dirac fermion.

arXiv comment15 pages, 1 figure, slightly corrected version

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Cited by in corpus (16)

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• How many surface modes does one see on the boundary of a Dirac material?
• Fractional Fermion Number and Hall Conductivity of Domain Walls
• Geometric Approach to 3D Interfaces at Strong Coupling
• Heat Kernel, Spectral Functions and Anomalies in Weyl Semimetals
• Anomaly and Superconnection
• Note on anomalous currents for a free theory
• Holographic Anomalous Chiral Current Near a Boundary
• Vacuum polarization near boundaries
• On the (im)possibility of Casimir repulsion between Chern-Simons surfaces
• Chiral magnetic effect at finite temperature in a field-theoretic approach
• Holographic Anomalous Current at a Finite Temperature
• Parity anomaly with impurities and the Pauli--Villars subtraction
• Remark on the synergy between the heat kernel techniques and the parity anomaly
• Enhancement of Anomalous Boundary Current by High Temperature
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings