3 research outputs found
Fermionic Operators from Bosonic Fields in 3+1 Dimensions
We present a construction of fermionic operators in 3+1 dimensions in terms
of bosonic fields in the framework of . The basic bosonic variables are
the electric fields and their conjugate momenta . 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
transformations are realized in this construction.Comment: 8 pages, two figures available on request, LA-UR-94-286
Bosonization in 2+1 dimensions without Chern - Simons attached
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 and , 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.Comment: 12 pages, LA-UR-93-1062, some misprints and algebraic errors
corrected, several comments adde