Dimensional expansions

It is proposed that the dimension D be used as a perturbation parameter. The coefficients in the resulting dimensional expansion, a series in powers of D, can be obtained in both quantum-mechanical and field-theoretic models. In this paper the first three terms in the dimensional expansion for the ground-state energy density for a self-interacting ${\mathrm{\phi }}^{2\mathit{K}}$ field theory are calculated. Dimensional expansions are shown to provide accurate nonperturbative analytic results.