Fermionic Operators from Bosonic Fields in 3+1 Dimensions

Details Fermionic Operators from Bosonic Fields in 3+1 Dimensions Fermionic Operators from Bosonic Fields in 3+1 Dimensions

1994-08-23

arxiv.org/abs/hep-th/9408128v1

Phys.Lett. B342 (1995) 381-386

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, two figures available on request, LA-UR-94-2863

Scientific paper

10.1016/0370-2693(94)01362-G

We present a construction of fermionic operators in 3+1 dimensions in terms of bosonic fields in the framework of $QED_4$. The basic bosonic variables are the electric fields $E_i$ and their conjugate momenta $A_i$. Our construction generalizes the analogous constuction of fermionic operators in 2+1 dimensions. Loosely speaking, a fermionic operator is represented as a product of an operator that creates a pointlike charge and an operator that creates an infinitesimal t'Hooft loop of half integer strength. We also show how the axial $U(1)$ transformations are realized in this construction.

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