Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- PART I NON-PERTURBATIVE METHODS IN TWO-DIMENSIONAL FIELD THEORY
- PART II TWO-DIMENSIONAL NON-PERTURBATIVE GAUGE DYNAMICS
- 8 Gauge theories in two dimensions – basics
- 9 Bosonized gauge theories
- 10 The 't Hooft solution of 2d QCD
- 11 Mesonic spectrum from current algebra
- 12 DLCQ and the spectra of QCD with fundamental and adjoint fermions
- 13 The baryonic spectrum of multiflavor QCD2 in the strong coupling limit
- 14 Confinement versus screening
- 15 QCD2, coset models and BRST quantization
- 16 Generalized Yang–Mills theory on a Riemann surface
- PART III FROM TWO TO FOUR DIMENSIONS
- References
- Index
9 - Bosonized gauge theories
Published online by Cambridge University Press: 07 September 2010
- Frontmatter
- Contents
- Preface
- Acknowledgements
- PART I NON-PERTURBATIVE METHODS IN TWO-DIMENSIONAL FIELD THEORY
- PART II TWO-DIMENSIONAL NON-PERTURBATIVE GAUGE DYNAMICS
- 8 Gauge theories in two dimensions – basics
- 9 Bosonized gauge theories
- 10 The 't Hooft solution of 2d QCD
- 11 Mesonic spectrum from current algebra
- 12 DLCQ and the spectra of QCD with fundamental and adjoint fermions
- 13 The baryonic spectrum of multiflavor QCD2 in the strong coupling limit
- 14 Confinement versus screening
- 15 QCD2, coset models and BRST quantization
- 16 Generalized Yang–Mills theory on a Riemann surface
- PART III FROM TWO TO FOUR DIMENSIONS
- References
- Index
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.
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- Non-Perturbative Field TheoryFrom Two Dimensional Conformal Field Theory to QCD in Four Dimensions, pp. 183 - 190Publisher: Cambridge University PressPrint publication year: 2010