Phase of the fermion determinant in QED_3 using a gauge invariant lattice regularization

Abstract

We use canonical formalism to study the fermion determinant in different three dimensional abelian gauge field backgrounds that contain non-zero magnetic and electric flux in order to understand the non-perturbative contributions to the parity-odd and parity-even parts of the phase. We show that a certain phase associated with free fermion propagation along a closed path in a momentum torus is responsible for the parity anomaly in a background with non-zero electric flux. We consider perturbations around backgrounds with non-zero magnetic flux to understand the structure of the parity-breaking perturbative term at finite temperature and mass.

arXiv comment20 pages, 6 figures; version accepted for publication in Phys. Rev. D

References in corpus (10)

• Chiral Fermions on the Lattice
• Vector like gauge theories with almost massless fermions on the lattice
• Non-Compact QED_3 with N_f=1 and N_f=4
• Non-compact QED_3 with N_f >=2
• On the Phase Structure of Many-Flavor QED${}_3$
• Gauge Invariance, Finite Temperature and Parity Anomaly in D=3
• Effective QED Actions: Representations, Gauge Invariance, Anomalies and Mass Expansions
• Overlap in odd dimensions
• Induced Parity Breaking Term at Finite Temperature
• QED${}_3$ on a space-time lattice: compact versus noncompact formulation

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• Parity anomaly cancellation in a three-dimensional QED with single massless Dirac fermion
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED
• A curious behavior of three-dimensional lattice Dirac operators coupled to monopole background