부산대학교 도서관

Yang-Mills theories in Coulomb gauge are often attributed with providing a rather direct access to bound states and other interesting quantities. However, even leading-order perturbative calculations in the conventional Lagrangian formulation are a formidable challenge. The authors of this paper develop an alternative approach, which is based on a perturbative expansion of the Schrödinger equation in a Hamiltonian formulation. Their aim is, in particular, to calculate correlation functions. \par To this end, the Schrödinger equation is expanded in powers of the coupling constant. This expansion permits a diagrammatical representation of the perturbative series. The authors use this series to determine the transverse gluon propagator, the ghost propagator, the Coulomb potential, and the ghost-gluon vertex. Under the assumption of multiplicative renormalizability, the divergent integrals which appear are dimensionally regulated and renormalized. This reproduces the known results of other approaches. In particular, the same value of the first coefficient of the beta function is obtained, irrespective of whether the running coupling is obtained from either the Coulomb potential or the ghost-gluon vertex. This result is used to determine renormalization-group improved correlation functions, and to determine the respective anomalous exponents. These are compared with results from lattice computations, which indicate that there are some discrepancies between the two, though this may depend on the particular lattice parameters. \par In total, the presentation is very clear, and the paper is very recommendable to anyone interested in Coulomb gauge calculations. However, whether this representation is advantageous, as the authors discuss, remains to be seen.