A nonperturbative variational approach to the vacuum structure in quantum chromodynamics

Gluon condensates, chiral symmetry breaking and pion wave-function

“…In the present section we shall recapitulate the nontrivial vacuum structure in quantum chromodynamics through Bogoliubov transformation as considered earlier [6] to set the notations, and derive some results.…”

“…In order to do the quantisation in Coulomb gauge, we write the electric field, G a 0i in terms of the transverse and longitudinal parts as [6] 5) where the form of f a is to be determined. In the Coulomb gauge the subsidiary condition and the equal time algebra for the gauge fields are given as [12] ∂ i W a i = 0 (2.6) and…”

“…We have proposed earlier an alternative scheme with a variational method which is nonperturbative [4,5], and uses off-shell gluons for the existence of a nontrivial vacuum structure [6]. Calculations are done in Coulomb gauge.…”

“…Calculations are done in Coulomb gauge. The inputs consist of the QCD Lagrangian, and QCD vacuum contains gluon condensates arising through a variational principle [6]. With a similar technique we have also considered chiral symmetry breaking in Nambu Jona Lasinio model, as well as for some quark antiquark phenomenological potentials used for hadron spectroscopy [7,8].…”

“…The techniques have been applied earlier to solvable cases to examine its reliability [5] as well as to physically more relevant ground state structures in high energy physics [6,9] and nuclear physics [10,11].…”