Hamiltonian approach to Yang-Mills theory in Coulomb gauge

Recent results obtained within the Hamiltonian approach to continuum Yang-Mills theory in Coulomb gauge are reviewed. INTRODUCTION There have been many attempts in the past to solve the Yang-Mills Schrödinger equation using gauge invariant wave functionals. Unfortunately, all these approaches have not been blessed with much success2. The reason is that it is extremely difficult to work with gauge invariant wave functionals. A much more economic way is to explicitly resolve Gauss’ law (which ensures gauge invariance of the wave functional) by fixing the gauge. For this purpose, the Coulomb gauge ~∂ ·~A = 0 is particularly convenient. In my talk, I would like to present a variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge [2]. Let me start by briefly summarizing the essential ingredients of the quantization of Yang-Mills theory in Coulomb gauge. In Coulomb gauge the space of (transversal) gauge orbits has a non-trivial metric, which is given by the Faddeev-Popov determinant J(A) = Det(−D̂i∂i), where D̂ab i = δ ∂i + Âab i , Â ab i = f Ai denotes the covariant derivative in the adjoint representation of the gauge group ( f acb is the structure constant). In Coulomb gauge the Yang-Mills Hamiltonian is given by [3] H = 1 2 ∫ J−1ΠJΠ+ 1 2 ∫