The MIT bag model Hamiltonian as an effective Hamiltonian of quantum chromodynamics

A possibility of derivation of the MIT bag model Hamiltonian from QCD is discussed. The bags are interpreted as wave packets of hadrons localized in the region x ≤ R where R is the bag radius. In the Fock space of gluodynamics a subspace P of the localized states is constructed and it is shown that projection of the Yang-Mills Hamiltonian into P has a representation in the Fock space PV of a Hamiltonian HV that depends on gluon fields defined inside a spherical cavity of radius R. The gluon fields obey boundary conditions. The one-to-one correspondence of vectors P and PV conserves Hermitian product, matrix elements of the Yang-Mills Hamiltonian between the states P are equal to the matrix elements of HV between the corresponding states of PV. Explicit form of the Hamiltonian HV is found. The MIT bag model Hamiltonian approximates in rough features the Hamiltonian HV