Lorentz Symmetric Quantum Field Theory for Symplectic Fermions

TL;DR

This paper develops a Lorentz-invariant quantum field theory for spin-half symplectic fermions in 2+1 dimensions, demonstrating its consistency and exploring potential interactions.

Contribution

It introduces a novel free quantum field theory for symplectic fermions with Lorentz symmetry, showing it satisfies key physical principles and analyzing possible interactions.

Findings

The theory is Lorentz invariant, causal, and unitary.

Fermionic spin-half fields can be quantized with a Klein-Gordon Lagrangian.

Possible interacting theories are briefly examined.

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.