Dimensional expansion for the delta-function potential. (English) Zbl 0943.81026
Summary: This paper examines an attractive delta-function potential in \(D\)-dimensional space, where \(D\) is regarded as an arbitrary complex number. The renormalized scattering amplitude is calculated for arbitrary \(D\) and is shown to be finite as \(D\to 2\). Dimensional expansions about \(D=0\) and \(D=2\) are obtained; these expansions have a non-zero radius of convergence.
MSC:
81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |