Nuclear Physics A468 (1987) 414-428 North-Holland. Amsterdam zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA A QUASIBOSON APPROXIMATION FOR AN INTERACTING MANY-GLUON SYSTEM P.O. HESS’ and R.D. VIOLLIER Institute of Theoretical Physics and Astrophysics, University of Cape Town, Rondebosch, 7700, Republic of South Africa Received 30 December 1985 (Revised 19 September 1986) Abstract: We develop a quasiboson approximation (QBA) to describe systems containing a large number of gluons. First the method is illustrated in the case of hypothetical gluons, which carry colour {l} and spin-l quantum numbers; subsequently, the method is generalized to include realistic colour {S} and spin-l gluons. We then apply the QBA to glueballs consisting of interacting Ml gluons. The gluon-gluon interaction is determined in second-order perturbation theory based on quantum chromodynamics in a cavity. In the case of a four-gluon system, the QBA leads to almost identical results as the exact calculation, while it becomes exact in the limit of an infinite number of gluons. Using the parameters of the MIT bag model, the energy of the lowest {l}O” state of an even number of gluons decreases quadratically with the number of gluons, thus signalling an instability of the perturbative vacuum against the formation of an Ml gluon condensate. 1. Introduction It is a well-known fact that quantum chromodynamics, the currently accepted theory of the strong interactions of quarks and gluons, allows in principle the existence of exotic hadrons which are composed of gluons rather than quarks and antiquarks. Even though there is little experimental evidence ‘) supporting this idea, exotic states may very well play a crucial role in the understanding of the properties of quantum chromodynamics and in particular the vacuum structure of the gauge theory which is based on the symmetry group SU(3),,,,,,. Recently ‘), we have pointed out that the many-gluon states can be classified according to the representations of the group chain U(24) =I U(8)OU(3). In this approach the colour degree of freedom is characterized by the representations of the U(8) = SU(3L,,, subchain and the spin degree of freedom is given in terms of the subchain U(3) 1 SU(2),+. We have introduced the coefficients of fractional parentage (cfp’s) which are defined as the overlap of the two-body with the many- body wavefunctions. Based on this method we have been able to evaluate the energies and quantum numbers of hadrons consisting of up to four gluons in a colour (1) state which interact via an arbitrary particle conserving two-body interaction. 1 Permanent address: Centro de Estudios Nucleares, UNAM, Circuit0 Exterior, Apdo. Postal 70-543, Del. Coyoacan, 04510, Mexico D.F. 037%9474/87/$03.50 @ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)