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Lorentz symmetric quantum field theory for symplectic fermions

J. Math. Phys. 50, 112301 (2009); doi:10.1063/1.3248256

Published 5 November 2009

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Dean J. Robinson, Eliot Kapit, and André LeClair
Newman Laboratory, Cornell University, Ithaca, New York 14850, USA
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, [script C][script P][script T] symmetry, and the Hermiticity and positive definiteness of the Hamiltonian. The global symmetry of the free theory is Sp(4)~=SO(5). Possible interacting theories of both the pseudo-Hermitian and Hermitian variety are then examined briefly. ©2009 American Institute of Physics
History: Received 27 April 2009; accepted 17 September 2009; published 5 November 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/112301/1
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KEYWORDS and PACS

Keywords
PACS
  • 11.30.Cp
    Lorentz and Poincaré invariance in particles and fields
  • 11.30.Er
    Charge conjugation, parity, time reversal, and other discrete symmetries in particles and fields
  • 11.30.Fs
    Global symmetries (e.g., baryon number, lepton number) in particles and fields
  • 11.10.Ef
    Lagrangian and Hamiltonian approach in field theory
  • YEAR: 2009

PUBLICATION DATA

ISSN:
0022-2488 (print)   1089-7658 (online)
Publisher:
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REFERENCES (11)
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