QUANTUM MECHANICS OF CONFINEMENT AND CHIRAL SYMMETRY BREAKING IN TWO-DIMENSIONAL QCD [chapter]

Alexei Nefediev
2000 Quark Confinement And The Hadron Spectrum III  
The system of light quark and heavy anti-quark source is studied in 1+1 QCD in the large N C limit. Making use of the modified Fock-Schwinger gauge allows to consider simultaneously the spectroscopical problem of the qQ bound states and the problem of the light quark Green function. The Dirac-type equation for the spectrum of the system is proved to be equivalent to the well-known 't Hooft one in the one body limit. The unitary transformation from the Dirac-Pauli representation to the
more » ... on to the Foldy-Wouthuysen one is carried out explicitly, and it is shown that the equation in the Foldy-Wouthuysen representation can be treated as a gap equation which defines the light quark self-energy in the modified Fock-Schwinger gauge. The Foldy-Wouthuysen angle is found to play the role of the Bogoliubov-Valatin one and to give the standard value of the chiral condensate. Connections of the given formalism to the standard four-dimensional QCD are outlined and discussed. * We adopt the following γ-matrix convention 2 : γ 0 = σ 3 , γ 1 = iσ 2 , γ 5 = σ 1 † The approach based on diagrammatic technics leads to the same results 4
doi:10.1142/9789812793713_0019 fatcat:af2hfzfmyvfkfesppdpagwmkva