Lorentz Symmetric Quantum Field Theory for Symplectic Fermions

Abstract

A free quantum field theory with Lorentz symmetry is derived for spin-half symplectic fermions in 2+1 dimensions. In particular, we show that fermionic spin-half fields may be canonically quantized in a free theory with a Klein-Gordon Lagrangian. This theory is shown to have all the required properties of a consistent free quantum field theory, namely causality, unitarity, adherence to the spin-statistics theorem, CPT symmetry, and the Hermiticity and positive definiteness of the Hamiltonian. The global symmetry of the free theory is Sp(4) $\simeq$ SO(5). Possible interacting theories of both the pseudo-Hermitian and Hermitian variety are then examined briefly.

11 pages. v2 with extra material

References in corpus (3)

• Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
• Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum Theory?
• A model of a 2d non-Fermi liquid with SO(5) symmetry, AF order, and a d-wave SC gap

Cited by in corpus (4)

• $T\bar{T}$-deformed Fermionic Theories Revisited
• Unitarity of Symplectic Fermion in $\alpha$-vacua with Negative Central Charge
• Higher-spin realization of a dS static patch/cut-off CFT correspondence
• Deconfined quantum criticality with internal supersymmetry