Fermionic Operators from Bosonic Fields in 3+1 Dimensions

Abstract

We present a construction of fermionic operators in 3+1 dimensions in terms of bosonic fields in the framework of $QE{D}_4$. 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.

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

References in corpus (3)

• New Look at QED${}_4$: the Photon as a Goldstone Boson and the Topological Interpretation of Electric Charge
• Bosonization in 2+1 dimensions without Chern - Simons attached
• Bosonization of $QE{D}_3$ with an induced Chern - Simons term

Cited by in corpus (3)

• Bosonization of Vector and Axial-Vector Currents in 3+1 Dimensions
• Decoupling Transformations in Path Integral Bosonization
• Loop Corrections and Bosonization Formulae