出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：The three-gluon and ghost-gluon vertices of Landau gauge Yang-Mills theory are investigated in
the low momentum regime. Due to ghost dominance in the infrared we can use the known power
law behavior for the propagators to determine analytically the complete momentum dependence
of the dressing functions. Besides a uniform, i. e. all momenta going to zero, divergence, we
find additional singularities, if one momentum alone goes to zero, while the other two remain
constant. At these asymmetric points we can extract additional infrared exponents, which corroborate
previous results and expand the known fixed point solution of Landau gauge Yang-Mills
theory, where the uniform infrared exponents for all vertex functions are known. Calculations in
two and three dimensions yield qualitatively similar results.
We find several dressing functions diverging like (p2)1−2k , if only the gluon momentum p goes
to zero. Of these many are longitudinal and do not contribute to Dyson-Schwinger equations. The
divergent transversal parts are additionally suppressed by the corresponding tensor. The longitudinal
dressing function of the ghost-gluon vertex behaves similarly, when the gluon momentum
becomes small compared to the ghost momentum, whereas all its other dressing functions vanish
at the asymmetric points. The uniform momentum dependence of the three-gluon vertex is
determined as (p2)−3k , while the ghost-gluon vertex stays finite in this limit.
