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UID:361@qft.physik.hu-berlin.de
DTSTART;TZID=Europe/Berlin:20140312T153000
DTEND;TZID=Europe/Berlin:20140312T163000
DTSTAMP:20140310T100640Z
URL:https://qft.physik.hu-berlin.de/next-seminars/120314/
SUMMARY:Hans-Peter Pavel\, JINR\, Dubna - Low energy QCD in terms of gauge 
 invariant dynamical variables
DESCRIPTION:Low energy QCD in terms of gauge invariant dynamical variables\
 nUsing a generalized polar decomposition of the gauge fields into gauge-ro
 tation and gauge-invariant parts\, which  Abelianises the Non-Abelian Gaus
 s-law constraints to be implemented\, a Hamiltonian formulation of low ene
 rgy QCD in terms of gauge invariant dynamical variables can be achieved.\n
 \nThe exact implementation of the Gauss laws reduces the colored spin-1 gl
 uons and spin-1/2 quarks to unconstrained colorless spin-0\, spin-1\, spin
 -2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respec
 tively.\n\nThe obtained physical Hamiltonian naturally admits a systematic
  strong-coupling expansion in powers of $\\lambda=g^{-2/3}$\, equivalent t
 o an expansion in the number of spatial derivatives.\n\nThe leading-order 
 term corresponds to non-interacting hybrid-glueballs\, whose low-lying spe
 ctrum can be calculated with high accuracy by solving the Schr\\"odinger-e
 quation of the Dirac-Yang-Mills quantum mechanics of spatially constant fi
 elds (at the moment only for the 2-color case).\n\nThe discrete glueball e
 xcitation spectrum shows a universal string-like behaviour with practicall
 y all excitation energy going in to the increase of the strengths of merel
 y two fields\, the "constant Abelian fields" corresponding to the zero-ene
 rgy valleys of the chromomagnetic potential. Inclusion of the fermionic de
 grees of freedom significantly lowers the spectrum and allows for the stud
 y of the sigma meson.\n\nHigher-order terms in $\\lambda$  lead to interac
 tions between the hybrid-glueballs and can be taken into account systemati
 cally using perturbation theory in $\\lambda$\, allowing for the study of 
 IR-renormalisation and Lorentz invariance.\n\nThe existence of the general
 ized polar decomposition used\, the position of the zeros of the correspon
 ding Jacobian (Gribov horizons)\, and the ranges of the physical variables
  can be investigated by solving a system of algebraic equations. Its exact
  solution for the case of one spatial dimension and first numerical soluti
 ons for two and three spatial dimensions indicate that there is a finite n
 umber of solutions separated by Gribov horizons.
CATEGORIES:Research Seminars
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