Triality and Dual Equivalence Between Dirac Field and Topologically Massive Gauge Field

Details Triality and Dual Equivalence Between Dirac Field and Topologically Massive Gauge Field Triality and Dual Equivalence Between Dirac Field and Topologically Massive Gauge Field

2006-02-27

arxiv.org/abs/hep-th/0602275v1

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, no figs

Scientific paper

It is proved that there exist a vector representation of Dirac's spinor field and in one sense it is equivalent to biquaternion (i.e. complexified quaternion) representation. This can be considered as a generalization of Cartan's idea of triality to Dirac's spinors. In the vector representation the first order Dirac Lagrangian is dual equivalent to the two order Lagrangian of topologically massive gauge field. The potential field which corresponds to the Dirac field is obtained by using master (or parent) action approach. The novel gauge field is self-dual and contains both anti-symmetric Lie and symmetric Jordan structure.

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