Bosonization in 2+1 dimensions without Chern - Simons attached

Abstract

We perform the complete bosonization of 2+1 dimensional QED with one fermionic flavor in the Hamiltonian formalism. The fermion operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify the regularization procedure involved in the definition of these operators, and calculate the fermionic bilinears and the energy - momentum tensor. The algebra of bilinears exhibits the Schwinger terms which also appear in perturbation theory. The bosonic Hamiltonian density is a local polynomial function of $A_i$ and $E_i$, and we check explicitly the Lorentz invariance of the resulting bosonic theory. Our construction is conceptually very similar to Mandelstam's construction in 1+1 dimensions, and is dissimilar from the recent bosonization attempts in 2+1 dimensions which hinge crucially on the existence of a Chern - Simons term.

12 pages, LA-UR-93-1062, some misprints and algebraic errors corrected, several comments added

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• Non Abelian Bosonization in Two and Three Dimensions
• Pure bosonic worldline path integral representation for fermionic determinants, non-Abelian Stokes theorem, and quasiclassical approximation in QCD
• Three dimensional fermionic determinants, Chern-Simons and nonlinear field redefinitions
• Fermionic Operators from Bosonic Fields in 3+1 Dimensions
• Fermionization, Number of Families