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9 - Bosonized gauge theories

Published online by Cambridge University Press:  07 September 2010

Yitzhak Frishman
Affiliation:
Weizmann Institute of Science, Israel
Jacob Sonnenschein
Affiliation:
Tel-Aviv University
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Summary

Bosonization, the equivalence map between two-dimensional fermionic and bosonic operators, was developed in Chapter 6. In fact several such maps have been described. The simplest one has been the abelian bosonization that maps the free theory of a Dirac fermion into that of a single real scalar field. The map includes in particular an explicit bosonic expression for the left and right chiral fermions (6.19), the vector and axial abelian currents (6.3) and for a mass term (6.22). Using these transformations it is straightforward to write the bosonized Lagrangian or Hamiltonian that corresponds to two-dimensional QED and QCD. By its nature the abelian bosonization is more adequate to the abelian theory of QED. The bosonized version of QED will be discussed in the next section. We then apply this bosonization to QCD2. Though it is possible to write QCD2 in an abelian bosonization formulation, it will turn out not to be very useful. Instead, we will use the non-abelian bosonization discussed in Section 6.3. For that purpose we will need to gauge the WZW action. Once this is done the bosonized version of massless flavored QCD2 follows easily. The massive case requires more care, as was explained in Section 6.3.3. Using the results of that section the full bosonized theory that corresponds to massive flavored QCD2 will be written down.

Type
Chapter
Information
Non-Perturbative Field Theory
From Two Dimensional Conformal Field Theory to QCD in Four Dimensions
, pp. 183 - 190
Publisher: Cambridge University Press
Print publication year: 2010

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