Time-localized projectors in String Field Theory with E-field

Phys.Rev. D71 (2005) 066007 We extend the analysis of hep-th/0409063 to the case of a constant electric field turned on the worldvolume and on a transverse direction of a D-brane. We show that time localization is still obtained by inverting the discrete eigenvalues of the lump solution. The lifetime of the unstable soliton is shown to depend on two free parameters: the b-parameter and the value of the electric field. As a by-product, we construct the normalized diagonal basis of the star algebra in $B_{\mu\nu}$-field background.