Lorentz Symmetric Quantum Field Theory for Symplectic Fermions

Details Lorentz Symmetric Quantum Field Theory for Symplectic Fermions Lorentz Symmetric Quantum Field Theory for Symplectic Fermions

2009-03-13

arxiv.org/abs/0903.2399v2

J.Math.Phys.50:112301,2009

Physics

High Energy Physics

High Energy Physics - Theory

11 pages. v2 with extra material

Scientific paper

10.1063/1.3248256

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.

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