Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1994-06-29
Z.Phys.A354:181-196,1996
Physics
High Energy Physics
High Energy Physics - Phenomenology
28 pages LaTeX, 4 figures appended as postscript files, UNITU-THEP-12/1994
Scientific paper
10.1007/s002180050031
The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu--Jona--Lasinio model the hidden gauge and massive Yang--Mills approaches to vector mesons are demonstrated to be linked by a special chiral transformation which removes the chiral field from the scalar--pseudoscalar sector. The chirally rotated axial vector meson field ($\tilde A_\mu$) transforms homogeneously under flavor rotations and may thus be dropped without violating chiral symmetry. The fermion determinant for static meson field configurations is computed by summing the discretized eigenvalues of the Dirac Hamiltonian. It is discussed how the local chiral transformation loses its unitary character in a finite model space. This technical issue proves to be crucial for the construction of the soliton within the Nambu--Jona--Lasinio model when the chirally rotated axial vector field is neglected. In the background of this soliton the valence quark is strongly bound, and its eigenenergy turns out to be negative. This important physical property which is usually generated only by non--vanishing axial vector is thus carried over by the simplification $\tilde A_\mu=0$.
Alkofer Reinhard
Reinhardt Hugo
Schlienz Juergen
Weigel Herbert
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